Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

A tabular source approach to modelling and simulating device and circuit noise in the time domain

Simulation of device and circuit noise at low frequencies is often carried out as part of a small‐signal ac analysis. Moreover, circuit simulators with rf analysis capabilities usually specify circuit performance in terms of S parameters and model high‐frequency noise in terms of noise waves and correlation matrices. It is also unusual to find circuit simulators that extend noise simulation to the time domain. This is particularly true for software packages developed from SPICE 2g6 or 3f5. This paper introduces a simple tabular noise source technique, which adds time‐domain noise to semiconductor device models and integrated circuit macromodels. The proposed technique is suitable for use with any general purpose circuit simulator. To demonstrate the power of the suggested approach the text describes time‐domain noise extensions to the SPICE diode, BJT, JFET, MOSFET and MESFET models. These noise extensions have been implemented and tested with the ‘Quite universal circuit simulator’ (Qucs). Copyright © 2011 John Wiley & Sons, Ltd.     

State‐space equations of regular and strictly topologically degenerate linear lumped time‐invariant networks: the multiport method

A new complete approach to the multiport formulation of the state‐space equations of uniquely solvable regular or strictly topologically degenerate linear lumped time‐invariant networks is presented. It is based on a Gedankenexperiment during which the topological structure of the original network is manipulated in various ways. The final method requires one to calculate the describing matrices of three homogeneous multiports (i.e. a capacitive, an inductive and a resistive one), which are obtained from the network of interest in a very simple manner. As a by‐product, the equivalent partitioned network is also derived. As an example of application, the state‐space equations of a fourth‐order strictly topologically degenerate network are provided. Copyright © 2001 John Wiley & Sons. Ltd.     

An accurate time‐domain model of transmission lines with frequency‐dependent parameters

Linear lossy two‐conductor transmission line can be modelled as dynamic two ports in the time domain, via the describing input and transfer impulse responses. This convolution technique is very effective when dealing with networks composed of transmission lines with frequency‐dependent parameters and non‐linear and/or time‐varying circuits. The paper carries out an accurate analysis of this model, in the most general case of lines with frequency‐dependent parameters. For such lines it is not possible to evaluate analytically the impulse responses, nor is it possible to catch them numerically, due to the presence of irregular terms, such as Dirac pulses, terms that numerically behave as Dirac pulses, and functions of the type 1/t^ρ with 0 < ρ <1. A simple method is proposed to evaluate exactly all the irregular terms of the impulse responses: once these irregular parts have been extracted, the regular remainders are easily evaluated numerically. This method is applied to analyse lines with frequency‐dependent parameters of practical interest, such as superconductor transmission lines, power lines above a finite conductivity ground, lines with frequency‐dependent dielectric losses and lines with normal and anomalous skin‐effect. Numerical simulations are carried out for illustration. Copyright © 2000 John Wiley & Sons, Ltd.     

On the simulation of fast settling charge pump PLLs up to fourth order

In this paper, we discuss three different models for the simulation of integer‐N charge‐pump phase‐locked loops (PLLs), namely the continuous‐time s‐domain and discrete time z‐domain approximations and the exact semi‐analytical time‐domain model. The limitations of the two approximated models are analyzed in terms of error in the computed settling time as a function of loop parameters, deriving practical conditions under which the different models are reliable for fast settling PLLs up to fourth order. Besides, output spectral purity analysis methods based upon the time‐domain model are introduced and the results are compared with those obtained by means of the s‐domain model in terms of phase noise and reference spur estimation. As a case study, we use the three models to analyze a fast switching PLL to be integrated in a frequency synthesizer for WiMedia MB‐OFDM UWB systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

An oscillatory noise‐shaped quantizer for time‐based continuous‐time sigma‐delta modulators

In this paper, a new type of an oscillatory noise‐shaped quantizer (NSQ) for time‐based continuous‐time sigma‐delta modulators is presented. The proposed NSQ is composed of an oscillatory voltage‐to‐time converter and a polyphase sampler. Using Tustin's transformation method and through the approximation of the comparator gain, a linearized model of the NSQ is introduced. This way, a novel realization of the first‐ and second‐order NSQ is presented. Its implementation is based on fully passive continuous‐time filters without needing any amplifier or power consuming element. The ploy‐phase sampler inside the NSQ is based on the combination of a time‐to‐digital and a digital‐to‐time converter. The layout of the proposed NSQ is provided in Taiwan Semiconductor Manufacturing Company 0.18 μm complementary metal‐oxide‐semiconductor 1P6M technology. The verification of the proposed NSQ is done via investigating both the system level and postlayout simulation results. Leveraging the proposed NSQ in an Lth‐order time‐based continuous‐time sigma‐delta modulator enhances the noise‐shaping order up to L + 2, confirming its superior effectiveness. This makes it possible to design high performance and wideband continuous‐time SDMs with low power consumption and relaxed design complexity.     

Absorbing boundary conditions for the FD‐TLM method : the perfectly matched layer and the one‐way equation technique

This paper investigates the absorbing boundary conditions for the frequency domain transmission line matrix method. Two approaches are presented, namely the perfectly matched layer (PML) technique and the one‐way wave equation. Concerning the PML technique, two‐dimensional and three‐dimensional transmission line matrix (TLM) nodes, already used in time domain, are exploited in frequency domain where a rigorous formulation of these PML–TLM nodes is presented. In addition, two types of one‐way wave operators are also transposed from time to frequency domain TLM approach: Taylor expansion and Higdon's boundary conditions. The simulation of a wideband matched load WR‐28 rectangular waveguide is presented for validation. Excellent results are obtained with a very thin PML layer. Results concerning one‐way operator techniques also show very good return loss performances. For instance, Higdon's boundary condition was extended beyond third‐order approximation, and a return loss better than 160 dB was obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

Frequency‐weighted model reduction via interpolation

We propose a numerical method of frequency‐weighted model reduction. The model to be reduced (an original model) is a stable SISO discrete‐time model described by high‐order state‐space equations. We design the reduced‐order model so that it can interpolate 1st‐ and 2nd‐order information of the original model at complex frequency points (interpolation points) in the unit circle. The characteristics of the reduced‐order model greatly depend on the choice of the interpolation points. The proposed model reduction method is a numerical one that chooses the interpolation points by searching in the unit circle to find the reduced‐order model such that L_∞‐norm of the reduction error is less than a prescribed value. This method has the following features that show that it is an effective numerical method of the frequency‐weighted model reduction. i) The reduced‐order model is guaranteed to be stable. ii) The procedure for finding the reduced‐order model is simple and requires a relatively small amount of computation. iii) The order of the reduced‐order model can be controlled by choosing the number of interpolation points. © 1998 Scripta Technica, Electr Eng Jpn, 126(2): 31–39, 1999     

Scalable models of microwave system responses using sequential sampling on unstructured grids

This paper presents two sequential sampling algorithms for the macromodeling of parameterized system responses in model‐dependent sampling frameworks. The construction of efficient algorithms for the automatic selection of samples for building scalable macromodels of frequency‐domain responses is addressed in this paper. The sequential sampling algorithms proposed here are tailored toward the application of local scalable macromodeling schemes on unstructured design space grids. Two pertinent examples are considered. For the first one, different algorithms are applied, and a comparison is made in terms of the number of samples generated, accuracy and CPU time. As a second example, four design variables are taken into account with one of the proposed algorithms, and the generated model is used in a frequency‐domain optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Linear time-varying systems analysis in wavelet domain

A new analysis method based on wavelet domain for linear time-varying systems is developed and introduced and it is called system analysis in wavelet domain (SAIWD). Linear time-varying systems described by a higher order differential equation or state-space representation are analyzed in wavelet domain. To solve system equations, they are transferred to wavelet domain by forming algebraic matrix–vector relations using the wavelet transform coefficients. These relations are achieved by defining operator matrices concerned with the commonly used time domain operators. Orthogonal and compact support wavelets provide a simple way to define these operator matrices. It is seen from the solved examples that the percentage error between the analytical and wavelet domain solutions is around 1% in total sampling points.     

Algorithm for detecting frequencies in multi‐sine signals by inductive generation

Prony's method is an approximation approach to decomposing a function into sum of exponents and thus is applicable to unknown frequencies estimation of signals. The concrete algorithms for estimating pure sine wave, triple tone, and quadruple tone have already been derived and presented. This paper aims at deriving the estimating algorithm for multi‐sine signals which consist of unknown sine waves. The new method of generating an algebraic algorithm for detecting unknown frequencies in the signals is derived by mathematical induction. The crux of the generation is dependent on the integer matrices induction. A handy method for generating the matrices is shown as well. Algorithms for the triple tone, quadruple tone, and the higher‐order tone are generated and verified. As a result, they are shown to be identical to the ordinary algorithms. Subjects on the application of the induced algorithm to practical frequency detection are discussed. The algorithm has both instantaneity in the time domain and higher resolution in the frequency domain, that is, the signal analysis by the algorithm can be performed without constraint of the uncertainty principle. An iterative solution for algebraic equation is dominant for calculation in the algorithm. Techniques for detecting frequencies in a multi‐sine of unknown order are also discussed. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(3): 27– 38, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20404     

Optimal design of lattice wave digital fractional‐order Butterworth filter

This letter presents the design of digital fractional‐order Butterworth filter (DFOBF) of order (n+α) , where n is an integer, and α ∈ (0,1) , from the perspective of optimal realization. The magnitude–frequency characteristic of the DFOBF is optimally modeled using the computationally efficient lattice wave digital filters (LWDFs). Design examples for the third‐ and fifth‐order LWDF‐DFOBFs with various values of n, α_, and cut‐off frequencies are presented.     

Output‐feedback co‐ordinated decentralized adaptive tracking: The case of MIMO subsystems with delayed interconnections

Exact decentralized output‐feedback Lyapunov‐based designs of direct model reference adaptive control (MRAC) for linear interconnected delay systems with MIMO subsystems are introduced. The design process uses a co‐ordinated decentralized structure of adaptive control with reference model co‐ordination which requires an exchange of signals between the different reference models. It is shown that in the framework of the reference model co‐ordination zero residual tracking error is possible, exactly as in the case with SISO subsystems. We develop decentralized MRAC on the base of a priori information about only the local subsystems gain frequency matrices without additional a priori knowledge about the full system gain frequency matrix. To achieve a better adaptation performance we propose proportional, integral time‐delayed adaptation laws. The appropriate Lyapunov–Krasovskii type functional is suggested to design the update mechanism for the controller parameters, and in order to prove stability. Two different adaptive DMRAC schemes are proposed, being the first asymptotic exact zero tracking results for linear interconnected delay systems with MIMO subsystems. Copyright © 2005 John Wiley & Sons, Ltd.     

Accelerating the transient simulation of semiconductor devices using filter‐bank transforms

Simulation of high frequency semiconductor devices, where non‐local and hot carrier transport cannot be ignored, requires solution of Poisson's equation and at least the first three moments of the Boltzmann transport equation (hydrodynamic transport model). These equations form non‐linear, coupled and time‐dependent partial differential equations. One of the most efficient solvers of such system of equations is decoupled solver. In conventional decoupled methods, the fully implicit, semi‐implicit and explicit methods are used to solve the equations. In fully or semi‐implicit schemes, the method is unconditionally stable for any Δt or for very large Δt compared to explicit scheme. Thus, these schemes are very suitable and efficient for transient simulations. But, using these techniques leads to a large system of linear equations. Here for the first time, a filter bank‐based preconditioning method is used to facilitate the iterative solution of this system. This method provides efficient preconditioners for matrices arising from discretizing of the PDEs, using finite difference techniques. Numerical results show that the condition number and iteration number are significantly reduced. The most important advantage of this preconditioner is its low computational complexity which can be reduced to O(N). Copyright © 2006 John Wiley & Sons, Ltd.     

An approach to digital implementation of continuous backstepping adaptive control for linear systems

This paper presents a solution to the problem of digitally implementing backstepping adaptive control for linear systems. The continuous‐time system to be controlled is given a discrete‐time representation in the δ‐operator. A discrete adaptive backstepping controller is then designed for such a discrete‐time model. The effect of the modelling error, generated by the sampling process, is accounted for in the parameter update law by a σ‐modification. It is shown that all the signals (discrete and continuous) of the closed loop are uniformly bounded, with a region of attraction which is a K_∞ function of the sampling rate. An upper bound on the asymptotic tracking error is then given, and shown to be proportional to the sampling period. Copyright © 1999 John Wiley & Sons, Ltd.     

Using modal series to analyze the transient response of oscillators

In this paper, a new form of Modal series is used to obtain the transient time‐domain response of oscillators. It is applicable to n‐dimensional systems and is not dependent on the existence of a small parameter in circuit's model. In addition, it provides an approximate analytical expression for the transient response instead of numerical solutions. It is valuable since the transient response of oscillators is not frequency stationary and therefore the FFT of numerical methods may not be so useful. The Colpitts oscillator is selected as a case study and a closed‐form expression for its transient response is derived which approximates the real response up to the steady state. Copyright © 2009 John Wiley & Sons, Ltd.     

A forward‐only recursion algorithm for MAP decoding of linear block codes

The evolution of digital mobile communications along with the increase of integrated circuit complexity has resulted in frequent use of error control coding to protect information against transmission errors. Soft decision decoding offers better error performance compared to hard decision decoding but on the expense of decoding complexity. The maximum a posteriori (MAP) decoder is a decoding algorithm which processes soft information and aims at minimizing bit error probability. In this paper, a matrix approach is presented which analytically describes MAP decoding of linear block codes in an original domain and a corresponding spectral domain. The trellis‐based decoding approach belongs to the class of forward‐only recursion algorithms. It is applicable to high rate block codes with a moderate number of parity bits and allows a simple implementation in the spectral domain in terms of storage requirements and computational complexity. Especially, the required storage space can be significantly reduced compared to conventional BCJR‐based decoding algorithms. Copyright © 2002 John Wiley & Sons, Ltd.     

Implementation of the stretched co‐ordinate‐based PML for waveguide structures in TLM

A novel implementation of the stretched co‐ordinate‐based perfectly matched layer (SCB PML) is presented to terminate waveguide structures in transmission‐line modelling (TLM). A generalized SCB PML, the complex frequency shifted PML (CFS PML) is also implemented to investigate its performance for evanescent waves. State variables in the Z‐domain are employed to obtain update equations for incident voltage pulses. Numerical results for a rectangular waveguide filled with a lossy medium as well as free space, and for a parallel plate waveguide are presented. Copyright © 2004 John Wiley & Sons, Ltd.