$$H_\infty $$ Model Reduction for the Distillation Column Linear System

In the paper, the problem of model reduction is considered for the distillation column linear system. For a given stable distillation column linear system, the objective is to find the construction of a reduced-order model, which approximates the original system well in the robust \(H_\infty \) performance. Some sufficient conditions to characterize the \(H_\infty \) norm bound error performance are proposed in terms of linear matrix inequalities (LMIs). Following the proposed projection approach, the \(H_\infty \) model reduction problem is solved, which casts the model reduction subject to LMIs constraints. Finally, a practical example of the distillation column linear system is provided to illustrate the effectiveness of the proposed method.     

Comparison of $$(1+\alpha )$$ Fractional-Order Transfer Functions to Approximate Lowpass Butterworth Magnitude Responses

Three fractional-order transfer functions are analyzed for differences in realizing (\(1+\alpha \)) order lowpass filters approximating a traditional Butterworth magnitude response. These transfer functions are realized by replacing traditional capacitors with fractional-order capacitors (\(Z=1/s^{\alpha }C\) where \(0\le \alpha \le 1\)) in biquadratic filter topologies. This analysis examines the differences in least squares error, stability, \(-\)3 dB frequency, higher-order implementations, and parameter sensitivity to determine the most suitable (\(1+\alpha \)) order transfer function for the approximated Butterworth magnitude responses. Each fractional-order transfer function for \((1+\alpha )=1.5\) is realized using a Tow–Thomas biquad a verified using SPICE simulations.     

5.18–7.42 GHz LC-VCO in subthreshold regime with low power low phase noise and immunity to PVT variations in 130 nm CMOS technology

In this paper, we propose an LC-VCO using automatic amplitude control and filtering technique to eliminate frequency noise around 2\(\omega _0\). The LC-VCO is designed with TSMC 130 nm CMOS RF technology, and biased in subthreshold regime in order to get more negative transconductance to overcome the losses in the LC-Tank and achieve less power consumption. The designed VCO operates at 5.17 GHz and can be tuned from 5.17 to 7.398 GHz, which is corresponding to 35.5% tuning range. The VCO consumes through it 495–440.5 \(\upmu\)W from 400 mV dc supply. This VCO achieves a phase noise of \(-\,122.3\) and \(-\,111.7\) dBc/Hz at 1 MHz offset from 5.17 and 7.39 GHz carrier, respectively. The calculated Figure-of-merits (FoM) at 1 MHz offset from 5.17 and 7.39 GHz is \(-\,199.7\) and \(-\,192.4\) dBc/Hz, respectively. And it is under \(-\,190.5\) dBc/Hz through all the tuning range. The FoM\(_T\) at 1 MHz offset from 5.17 GHz carrier is \(-\,210.6\) dBc/Hz. The proposed design was simulated for three different temperatures (\(-\,55\), 27, \(125\,^{\circ }\hbox {C}\)), and three supply voltages (0.45, 0.4, 0.35 V), it was concluded that the designed LC-VCO presents high immunity to PVT variations, and can be used for multi-standard wireless LAN communication protocols 802.11a/b/g.     

Design and Performance Study of Dynamic Fractors in Any of the Four Quadrants

A fractor is a simple fractional-order system. Its transfer function is \(1/Fs^{\alpha }\); the coefficient, F, is called the fractance, and \(\alpha \) is called the exponent of the fractor. This paper presents how a fractor can be realized, using RC ladder circuit, meeting the predefined specifications on both F and \(\alpha \). Besides, commonly reported fractors have \(\alpha \) between 0 and 1. So, their constant phase angles (CPA) are always restricted between \(0^{\circ }\) and \(-90^{\circ }\). This work has employed GIC topology to realize fractors from any of the four quadrants, which means fractors with \(\alpha \) between \(-\)2 and +2. Hence, one can achieve any desired CPA between \(+180^{\circ }\) and \(-180^{\circ }\). The paper also exhibits how these GIC parameters can be used to tune the fractance of emulated fractors in real time, thus realizing dynamic fractors. In this work, a number of fractors are developed as per proposed technique, their impedance characteristics are studied, and fractance values are tuned experimentally.     

Electrical Transport Mechanisms and Photoconduction in Undoped Crystalline Flash-Evaporated Lead Iodide Thin Films

The flash-evaporation technique was utilized to fabricate undoped 1.35-μm and 1.2-μm thick lead iodide films at substrate temperatures \( T_{\rm{s}} = 150 \)°C and 200°C, respectively. The films were deposited onto a coplanar comb-like copper (Cu-) electrode pattern, previously coated on glass substrates to form lateral metal–semiconductor–metal (MSM-) structures. The as-measured constant-temperature direct-current (dc)-voltage (\( I\left( {V;T} \right) - V \)) curves of the obtained lateral coplanar Cu-PbI₂-Cu samples (film plus electrode) displayed remarkable ohmic behavior at all temperatures (\( T = 18 - 90\,^\circ {\hbox{C}} \)). Their dc electrical resistance \( R_{\rm{dc}} (T \)) revealed a single thermally-activated conduction mechanism over the temperature range with activation energy \( E_{\rm{act}} \approx 0.90 - 0.98 \,{\hbox{eV}} \), slightly less than half of room-temperature bandgap energy \( E_{\rm{g}} \) (\( \approx \,2.3\, {\hbox{eV}} \)) of undoped 2H-polytype PbI₂ single crystals. The undoped flash-evaporated \( {\hbox{PbI}}_{\rm{x}} \) thin films were homogeneous and almost stoichiometric (\( x \approx 1.87 \)), in contrast to findings on lead iodide films prepared by other methods, and were highly crystalline hexagonal 2H-polytypic structure with c-axis perpendicular to the surface of substrates maintained at \( T_{\rm{s}} { \gtrsim }150^\circ {\hbox{C}} \). Photoconductivity measurements made on these lateral Cu-PbI₂-Cu-structures under on–off visible-light illumination reveal a feeble photoresponse for long wavelengths (\( \lambda > 570\,{\hbox{nm}} \)), but a strong response to blue light of photon energy \( E_{\rm{ph}} \) \( \approx \,2.73 \, {\hbox{eV}} \) (\( > E_{\rm{g}} \)), due to photogenerated electron–hole (e–h) pairs via direct band-to-band electronic transitions. The constant-temperature/dc voltage current–time \( I\left( {T,V} \right) - t \) curves of the studied lateral PbI₂ MSM-structures at low ambient temperatures (\( T < 50^\circ {\hbox{C}} \)), after cutting off the blue-light illumination, exhibit two trapping mechanisms with different relaxation times. These strongly depend on \( V \) and \( T \), with thermally generated charge carriers in the PbI₂ mask photogenerated (e–h) pairs at higher temperatures.     

Minimizing the Two-Round Even–Mansour Cipher

The r-round (iterated) Even–Mansour cipher (also known as key-alternating cipher) defines a block cipher from r fixed public n-bit permutations \(P_1,\ldots ,P_r\) as follows: Given a sequence of n-bit round keys \(k_0,\ldots ,k_r\), an n-bit plaintext x is encrypted by xoring round key \(k_0\), applying permutation \(P_1\), xoring round key \(k_1\), etc. The (strong) pseudorandomness of this construction in the random permutation model (i.e., when the permutations \(P_1,\ldots ,P_r\) are public random permutation oracles that the adversary can query in a black-box way) was studied in a number of recent papers, culminating with the work of Chen and Steinberger (EUROCRYPT 2014), who proved that the r-round Even–Mansour cipher is indistinguishable from a truly random permutation up to \(\mathcal {O}(2^{\frac{rn}{r+1}})\) queries of any adaptive adversary (which is an optimal security bound since it matches a simple distinguishing attack). All results in this entire line of work share the common restriction that they only hold under the assumption that the round keys \(k_0,\ldots ,k_r\) and the permutations \(P_1,\ldots ,P_r\) are independent. In particular, for two rounds, the current state of knowledge is that the block cipher \(E(x)=k_2\oplus P_2(k_1\oplus P_1(k_0\oplus x))\) is provably secure up to \(\mathcal {O}(2^{2n/3})\) queries of the adversary, when \(k_0\), \(k_1\), and \(k_2\) are three independent n-bit keys, and \(P_1\) and \(P_2\) are two independent random n-bit permutations. In this paper, we ask whether one can obtain a similar bound for the two-round Even–Mansour cipher from just one n-bit key and one n-bit permutation. Our answer is positive: When the three n-bit round keys \(k_0\), \(k_1\), and \(k_2\) are adequately derived from an n-bit master key k, and the same permutation P is used in place of \(P_1\) and \(P_2\), we prove a qualitatively similar \(\widetilde{\mathcal {O}}(2^{2n/3})\) security bound (in the random permutation model). To the best of our knowledge, this is the first “beyond the birthday bound” security result for AES-like ciphers that does not assume independent round keys.     

A PAPR reduction scheme based on a new spreading code in optical direct detection OFDM system

In this paper, we propose and experimentally demonstrate a peak-to-average power ratio (PAPR) reduction scheme based on a new spreading code in direct detection optical orthogonal frequency division multiplexing (OFDM) system. The new spreading code with low cross correlation and high auto-correlation can support \(2N+1\) users. Thus, \(2N+1\) users or data symbols can be transmitted over only N subcarriers. The experimental results show that, after transmission over 70 km single-mode fiber, at the bit error rate of \(10^{-3}\), with fiber launch power of 2.75 dBm, the receiver sensitivity can be improved 2.1 dB by using the proposed scheme based on new spreading code. The PAPR can be reduced about 4.6 dB, compared with the original OFDM signal at a complementary cumulative distribution function of \(10^{-4}\).     

Two-channel perfect reconstruction (PR) quadrature mirror filter (QMF) bank design using logarithmic window function and spline function

In this work, two-channel perfect reconstruction quadrature mirror filter (QMF) bank has been proposed based on the prototype filter using windowing method. A novel window function based on logarithmic function along with the spline function is utilized for the design of prototype filter. The proposed window has a variable parameter ‘\(\alpha \)’, which varies the peak side lobe level and rate of fall-off side lobe level which in turn affects the peak reconstruction error (PRE) and amplitude distortion (\(e_{am}\)) of the QMF bank . The transition width of the prototype is controlled by the spline function using the parameter ‘\(\mu \)’. The perfect reconstruction condition is satisfied by setting the cutoff frequency (\(\omega _{c}\)) of the prototype low-pass filter at ‘\(\pi /2\)’. The performance of the proposed design method has been evaluated in terms of mean square error in the pass band, mean square error in the stop band, first side lobe attenuation (\(A_{1}\)), peak reconstruction error (PRE) and amplitude error (\(e_{am}\)) for different values of ‘\(\alpha \)’ and ‘\(\mu \)’. The results are provided and compared with the existing methods.     

State Feedback $$L_1$$-Gain Control of Positive 2-D Continuous Switched Delayed Systems Via State-Dependent Switching

This paper investigates the stability and \(L_1\)-gain control of two-dimensional (2-D) continuous positive switched delayed systems. Firstly, by constructing an appropriate co-positive Lyapunov–Krasovskii functional, a sufficient condition for asymptotical stability of the system under consideration is derived. Secondly, \(L_1\)-gain performance analysis of the underlying system is investigated. Thirdly, a design methodology for state feedback controller is proposed to ensure that the closed-loop system is asymptotically stable with \(L_1\)-gain performance. Finally, an example is provided to show the effectiveness of the proposed method.     

Automata Evaluation and Text Search Protocols with Simulation-Based Security

This paper presents efficient protocols for securely computing the following two problems: (1) The fundamental problem of pattern matching. This problem is defined in the two-party setting, where party \(P_1\) holds a pattern and party \(P_2\) holds a text. The goal of \(P_1\) is to learn where the pattern appears in the text, without revealing it to \(P_2\) or learning anything else about \(P_2\)’s text. This problem has been widely studied for decades due to its broad applicability. We present several protocols for several notions of security. We further generalize one of our solutions to solve additional pattern matching-related problems of interest. (2) Our construction from above, in the malicious case, is based on a novel protocol for secure oblivious automata evaluation which is of independent interest. In this problem, party \(P_1\) holds an automaton and party \(P_2\) holds an input string, and they need to decide whether the automaton accepts the input, without learning anything else. Our protocol obtains full security in the face of malicious adversaries.     

The Security of Tandem-DM in the Ideal Cipher Model

We prove that Tandem-DM, one of the two “classical” schemes for turning an n-bit blockcipher of 2n-bit key into a double-block-length hash function, has birthday-type collision resistance in the ideal cipher model. For \(n=128\), an adversary must make at least \(2^{120.87}\) blockcipher queries to achieve chance 0.5 of finding a collision. A collision resistance analysis for Tandem-DM achieving a similar birthday-type bound was already proposed by Fleischmann, Gorski and Lucks at FSE 2009. As we detail, however, the latter analysis is wrong, thus leaving the collision resistance of Tandem-DM as an open problem until now. Our analysis exhibits a novel feature in that we introduce a trick never used before in ideal cipher proofs. We also give an improved bound on the preimage security of Tandem-DM. For \(n=128\), we show that an adversary must make at least \(2^{245.99}\) blockcipher queries to achieve chance 0.5 of inverting a randomly chosen point in the range. Asymptotically, Tandem-DM is proved to be preimage resistant up to \(2^{2n}/n\) blockcipher queries. This bound improves upon the previous best bound of \({{\varOmega }}(2^n)\) queries and is optimal (ignoring log factors) since Tandem-DM has range of size \(2^{2n}\).     

On the equivalence of multivariate polynomial matrices

The equivalence of system is an important concept in multidimensional (\(n\)D) system, which is closely related to equivalence of multivariate polynomial matrices. This paper mainly investigates the equivalence of some \(n\)D polynomial matrices, several new results and conditions on the reduction by equivalence of a given \(n\)D polynomial matrix to its Smith form are obtained.     

Finite frequency $$H_\infty $$ control of 2-D continuous systems in Roesser model

This paper investigates the finite frequency (FF) \(H_\infty \) control problem of two-dimensional (2-D) continuous systems in Roesser Model. Our attention is focused on designing state feedback controllers guaranteeing the bounded-input-bounded-output stability and FF \(H_\infty \) performance of the corresponding closed-loop system. A generalized 2-D Kalman-Yakubovich-Popov (KYP) lemma is presented for 2-D continuous systems. By the generalized 2-D KYP lemma, the existence conditions of \(H_\infty \) controllers are obtained in terms of linear matrix inequalities. Two examples are given to validate the proposed methods.     

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

This paper considers the asymptotical synchronization and \(H_\infty \) synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov–Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the \(H_\infty \) synchronization problem is also considered. The equivalence between the \(H_\infty \) stability of decoupled synchronization error dynamical systems and the \(H_\infty \) synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the \(H_\infty \) stabilization is presented, which guarantees the \(H_\infty \) synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.     

Direction of arrival estimation via reweighted $$l_1$$ norm penalty algorithm for monostatic MIMO radar

In this paper, a reweighted \(l_1\) norm penalty algorithm for direction of arrival (DOA) estimation in monostatic multiple-input multiple-output radar is proposed. In the proposed method, exploiting the inherent multidimensional structure of received data after matched filtering, the singular value decomposition (SVD) technique of the data matrix is employed to reduce the dimension of the received signal. Then a novel weight matrix is designed for reweighting the \(l_1\) norm minimization by exploiting the coefficients of the reduced-dimensional Capon (RD-Capon) spatial spectrum. The proposed algorithm enhances the sparsity of the solution by the reweighted \(l_1\) norm constraint minimization, and the DOAs can be estimated by finding the non-zero rows of the recovered matrix. Owing to utilizing the SVD technique and the novel weight matrix, the proposed algorithm can provide better angle estimation performance than RD-Capon and \(l_1\)-SRACV algorithms. Furthermore, it is suitable for coherent sources and has a low sensitivity to the incorrect determination of the source numbers. The effectiveness and superior performance of the proposed algorithm are demonstrated by numerical simulations.     

Error performance of optically preamplified hybrid BPSK-PPM systems with transmitter and receiver imperfections

In this paper, we investigate the impact of the transmitter finite extinction ratio and the receiver carrier recovery phase offset on the error performance of two optically preamplified hybrid M-ary pulse position modulation (PPM) systems with coherent detection. The first system, referred to as PB-mPPM, combines polarization division multiplexing (PDM) with binary phase-shift keying and M-ary PPM, and the other system, referred to as PQ-mPPM, combines PDM with quadrature phase-shift keying and M-ary PPM. We provide new expressions for the probability of bit error for PB-mPPM and PQ-mPPM under finite extinction ratios and phase offset. The extinction ratio study indicates that the coherent systems PB-mPPM and PQ-mPPM outperform the direct-detection ones. It also shows that at \(P_b=10^{-9}\) PB-mPPM has a slight advantage over PQ-mPPM. For example, for a symbol size \(M=16\) and extinction ratio \(r=30\) dB, PB-mPPM requires 0.6 dB less SNR per bit than PQ-mPPM to achieve \(P_b=10^{-9}\). This investigation demonstrates that PB-mPPM is less complex and less sensitive to the variations of the offset angle \(\theta \) than PQ-mPPM. For instance, for \(M=16\), \(r=30\) dB, and \(\theta =10^{\circ }\) PB-mPPM requires 1.6 dB less than PQ-mPPM to achieve \(P_b=10^{-9}\). However, PB-mPPM enhanced robustness to phase offset comes at the expense of a reduced bandwidth efficiency when compared to PQ-mPPM. For example, for \(M=2\) its bandwidth efficiency is 60 % that of PQ-mPPM and \(\approx 86\,\%\) for \(M=1024\). For these reasons, PB-mPPM can be considered a reasonable design trade-off for M-ary PPM systems.     

Intermittent Fault Diagnosability of Hyper Petersen Network

The problem of permanent fault diagnosis has been discussed widely, and the diagnosability of many well-known networks have been explored. Faults of a multiprocessor system generally include permanent and intermittent, with intermittent faults regarded as the most challenging to diagnose. In this paper, we investigate the intermittent fault diagnosability of hyper Petersen networks. First, we derive that an \(n\)-dimensional hyper Petersen network \(HP_{n}\) with fault-free edges is \((n - 1)_{i}\)-diagnosable under the PMC model. Then, we investigate the intermittent fault diagnosability of \(HP_{n}\) with faulty edges under the PMC model. Finally, we prove that an \(n\)-dimensional hyper Petersen network \(HP_{n}\) is \((n - 2)_{i}\)-diagnosable under the MM* model.     

Mixed RF/FSO bidirectional system achieving spectral efficiency

The performance of two-way relay (TWR)-assisted mixed radio-frequency/free-space optical (RF/FSO) system is evaluated in this letter. The proposed system employs decode-and-forward relaying phenomena where the relay is basically an interfacing node between two source nodes \(S_1\) and \(S_2\), where \(S_1\) supports RF signal, while \(S_2\) supports FSO signal. The TWR-assisted system helps in achieving spectral efficiency by managing bidirectional communication in three time slots, thus maximizing the achievable rate of the network. The RF link is subjected to generalized \(\eta -\mu \) distribution, and the optical channel is affected by path loss, pointing errors and gamma–gamma (gg) distributed atmospheric turbulence. The novel expressions for the probability density function and cumulative distribution function of the equivalent end-to-end signal-to-noise ratio (SNR) are derived. Capitalizing on these derived statistics of end-to-end SNR, the expressions of outage probability and the bit-error rate for different binary modulations and M-ary modulations are provided.     

Highly efficient nonlinear regression for big data with lexicographical splitting

This paper considers the problem of online piecewise linear regression for big data applications. We introduce an algorithm, which sequentially achieves the performance of the best piecewise linear (affine) model with optimal partition of the space of the regressor vectors in an individual sequence manner. To this end, our algorithm constructs a class of \(2^D\) sequential piecewise linear models over a set of partitions of the regressor space and efficiently combines them in the mixture-of-experts setting. We show that the algorithm is highly efficient with computational complexity of only \(O(mD^2)\), where m is the dimension of the regressor vectors. This efficient computational complexity is achieved by efficiently representing all of the \(2^D\) models using a “lexicographical splitting graph.” We analyze the performance of our algorithm without any statistical assumptions, i.e., our results are guaranteed to hold. Furthermore, we demonstrate the effectiveness of our algorithm over the well-known data sets in the machine learning literature with computational complexity fraction of the state of the art.     

Stabilization of Discrete-time Fuzzy Systems Via Delta Operators and its Application to Truck–Trailer Model

This paper addresses the problem of robust \(L_2{-}L_\infty \) control in delta domain for a class of Takagi–Sugeno (TS) fuzzy systems with interval time-varying delays and disturbance input. In particular, the system under study involves state time delay, uncertainties and fast sampling period \(\mathcal {T}\). The main aim of this work was to design a \(L_2{-}L_\infty \) controller such that the proposed TS fuzzy system is robustly asymptotically stable with a \(L_2{-}L_\infty \) prescribed performance level \(\gamma >0\). Based on the proper Lyapunov–Krasovskii functional (LKF) involving lower and upper bound of time delay and free-weighting technique, a new set of delay-dependent sufficient conditions in terms of linear matrix inequalities (LMIs) are established for obtaining the required result. The result reveals that the asymptotic stability is achieved quickly when the sampling frequency is high. Finally, a numerical example based on the truck–trailer model is given to demonstrate the effectiveness and potential of the proposed design technique.