On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.Notation real number field - complex number field - x x=(x ₁,x ₂,...,x _n ) ^T R ⁿ - x ^T transpose of vectorx - x* complex conjugate transpose of vectorx - Re(·) real part of (·) - x norm of vectorx; x=(x*x)^1/2 - A ^T transpose of matrixA - A* complex conjugate transpose of matrixA - ¯(·) maximal absolute value of eigenvalue of matrixA - (A) matrix measure of matrixA; (A)=¯((A + A*)/2) - A induced norm of matrix A; A=[¯(A*A)]^1/2 - ¦a_ij ¦ absolute value of element a_ij - ¦ A¦ {¦a_ij¦} for matrix A={a_ij} - A >B a_ij > b_ij for alli andj where A={a_ij} andB={b_ij} - z complex number - ¯z complex conjugate ofz Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.     

The prime and generalized nullspaces of right regular pencils

The classical notion of the -generalized nullspace, defined on a matrixA R ^n×n,where is an eigenvalue, is extended to the case of ordered pairs of matrices(F, G), F, G R ^m×nwhere the associated pencilsF – G is right regular. It is shown that for every C {} generalized eigenvalue of (F, G), an ascending nested sequence of spaces {P ⁱ ,i=1, 2,...} and a descending nested sequence of spaces {ie495-02 i=1, 2,...} are defined from the -Toeplitz matrices of (F, G); the first sequence has a maximal elementM ^* , the -generalized nullspace of (F, G), which is the element of the sequence corresponding to the index , the -index of annihilation of (F, G), whereas the second sequence has the first elementP ^* as its maximal element, the -prime space of (F, G). The geometric properties of the {M ⁱ ,i=1, 2,..., and {P ⁱ ,i=1, 2,...sets, as well as their interrelations are investigated and are shown to be intimately related to the existence of nested basis matrices of the nullspaces of the -Toeplitz matrices of (F, G). These nested basis matrices characterize completely the geometry ofM ^* and provide a systematic procedure for the selection of maximal length linearly independent vector chains characterizing the-Segre characteristic of (F, G).     

Symmetry relations in multidimensional Fourier transform pairs

A relation between the types of symmetries that exist in signal and Fourier transform domain representations is derived for continuous as well as discrete domain signals. The symmetry is expressed by a set of parameters, and the relations derived in this paper will help to find the parameters of a symmetry in the signal or transform domain resulting from a given symmetry in the transform or signal domain respectively. A duality among the relations governing the conversion of the parameters of symmetry in the two domains is also brought to light. The application of the relations is illustrated by a number of two-dimensional examples.Notation R the set of real numbers - R ^m R × R × ... × R m-dimensional real vector space - continuous domain real vector - L {¦ – _i , i = 1,2,..., m} - m-dimensional frequency vector - W { – _i ,i=1,2,..., m} - m-dimensional normalized frequency vector - _P {¦ – _i , i=1,2,...,m} - g(ol) g (₁,₂,..., _m ) continuous domain signal - () ( _{1 2},..., _m )=G (j ₁,j ₂,..., j _m ) Fourier transform ofg (ol) - (A,b,,,) parameters ofT- symmetry - N the set of integers - N ^m N × N × ... × N m-dimensional integer vector spacem-dimensional lattice - h(n) h (n ₁,.,n _m ) discrete domain signal - H() Fourier transform ofh (n) - v ₁,v ₂,..., v_m m sample-direction and interval vectors - V (v ₁ v ₂ ...v _m ) sampling basis matrix - [x]^* complex conjugate ofx - detA determinant ofA - X {x¦ – x _i , i=1,2,..., m} - A ^–t [A ^–1] ^t ,t stands for transpose This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739 to M. N. S. Swamy and in part by Tennessee Technological University under its Faculty Research support program to P. K. Rajan.     

On the distribution of characteristics in bijective mappings

Differential cryptanalysis is a method of attacking iterated mappings based on differences known as characteristics. The probability of a given characteristic is derived from the XOR tables associated with the iterated mapping. If is a mapping : Z ₂ ^m , then for each , X, Y Z ₂ ^m the XOR table for gives the number of input pairs of difference X=X+X for which gp(X)+(X)=Y.The complexity of a differential attack depends upon two properties of the XOR tables: the density of zero entries in the table, and the size of the largest entry in the table. In this paper we present the first results on the expected values of these properties for a general class of mappings . We prove that if : Z ₂ ^m Z ₂ ^m is a bijective mapping, then the expected size of the largest entry in the XOR table for is bounded by 2m, while the fraction of the XOR table that is zero approaches e ^–1/2=0.60653. We are then able to demonstrate that there are easily constructed classes of iterated mappings for which the probability of a differential-like attack succeeding is very small.The author is presently employed by the Distributed System Technology Center, Brisbane, Australia.     

Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part I: Conservation laws

This paper is the first in a two part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops from the geometric coordinate-free point of view of differentiable manifolds. Given such a nonlinear networkN, with °₀ equal to the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops, we establish the following: (i) circuit theoretic sufficient conditions to guarantee that the set ⁰, of equilibrium points is a ₀-dimensional submanifold of the state space ofN; (ii) circuit theoretic sufficient conditions for the condition thatN has ₀ independent conservation laws and hence that through each point of the state space ofN, there passes a codimension ₀ invariant submanifold ^* of the network dynamics; (iii) circuit theoretic sufficient conditions to guarantee that the manifolds ^* and ⁰ intersect transversely.This work was supported by the Natural Sciences and Engineering Research Council of Canada, under Grant Number A7113, and by scholarships from the Natural Sciences and Engineering Research Council of Canada and the Ontario Provincial Government.     

Pervasive Home Environments

For decades, technologists have been promising the intelligent house. The vision is usually portrayed as a house filled with technology which will do the dweller's bidding and take all domestic drudgery out of their lives. The truly intelligent house is still some way off, but the emergence of broadband, availability of faster, smaller and ever cheaper computing equipment and a variety of wired and wireless network technologies are enabling technologies that bring this vision closer to reality. These technology trends lead to the concept that computing and other smart devices will become pervasive, fully networked and disappear into the infrastructure of the home. People will carry out their tasks unaware of the complexity of the infrastructure that supports their activities in much the same way as people today use mains electricity.This paper introduces these concepts and discusses the technological challenges to be overcome. We present our vision of the pervasive home environment where inhabitants can focus on tasks rather than the technology: I need to create X and send it to Y rather than I need to use this computer and this application which needs access to service A and resource B. Although this sounds simple, the environment needs to understand who I is, and who or what Y is. Appropriate permissions must be in place and resources allocated, if available. The most appropriate interface for the task and user must be determined.The pervasive, intelligent home will make available new ways to access and share information. It will herald new services, such as care and support of people in the home, entertainment, educational and security services. The final part of the paper discusses the commercial opportunities and challenges which must be met, not least the need for industry to agree on open standards and interfaces.     

A Difference Reference Voltage Buffer for ΔΣ-Converters

An open loop architecture for a reference voltage buffer in -converters is presented to achieve fast-settling, since the settling time of the references plays an important role in the global performance of sampled data converters. This design has been tested on a 2-1 -converter with an on-chip bandgap reference increasing the input related dynamic range up to 93.4 dB for a bandwidth of 99 kHz.     

Systematic Width-and-Length Dependent CMOS Transistor Mismatch Characterization and Simulation

This paper presents a methodology for characterizing the random component of transistor mismatch in CMOS technologies. The methodology is based on the design of a special purpose chip which allows automatic characterization of arrays of NMOS and PMOS transistors of different sizes. Up to 30 different transistor sizes were implemented in the same chip, with varying transistors width W and length L. A simple strong inversion large signal transistor model is considered, and a new five parameters MOS mismatch model is introduced. The current mismatch between two identical transistors is characterized by the mismatch in their respective current gain factors /, V _TO threshold voltages , bulk threshold parameters , and two components for the mobility degradation parameter mismatch ₀ and _e. These two components modulate the mismatch contribution differently, depending on whether the transistors are biased in ohmic or in saturation region. Using this five parameter mismatch model, an extraordinary fit between experimental and computed mismatch is obtained, including minimum length (1 m) transistors for both ohmic and saturation regions. Standard deviations for these five parameters are obtained as well as their respective correlation coefficients, and are fitted to two dimensional surfaces f(W, L) so that their values can be predicted as a function of transistor sizes. These functions are used in an electrical circuit simulator (Hspice) to predict transistor mismatch. Measured and simulated data are in excellent agreement.     

The Problem with Disruption

Back in January 1995 Clayton Christensen and Joseph Bower wrote an article, Disruptive Technologies: catching the wave, in the Harvard Business Review, in which they argued: No matter the industry, a corporation consists of business units with finite life spans: the technological and market bases of any business will eventually disappear. Good businesses will often be adept at managing a process of incremental improvement, but this kind of incremental change, what they call sustaining technologies, is not the focus of this paper but rather disruptive technologies, which change the rules and leave established businesses with nowhere to go.     

Higher-order terms in asymptotic expansion for information loss in quantized random processes

Uniform quantization of random vectors onto -grids ⁿ is considered. Higherorder terms in asymptotic expansions for the entropy of the -quantized random vector and for the loss of the mutual information between two random vectors under such quantization as 0+are obtained. The coefficients in these asymptotics are explicitly calculated for Gaussian distributed vectors. Taken for initial segments of stationary Gaussian sequences, these factors have limit average values per unit of time. For such sequences governed by state-space equations, computation of these average values is reduced to solutions of algebraic matrix Riccati and Lyapunov equations.Work supported by the Australian Research Council grant A 4970 2246.     

High Dynamic Range Design for ΣΔM with Wide Input Ranges

A new design algorithm is introduced to improve the input ranges of Sigma-Delta Modulation (M). Modified digital error correction techniques are proposed and employed to carry out the wide range DAC of a modulator. This design algorithm includes the advantages from both single-bit M and multi-bit M. This paper utilizes a second order lowpass modulator as an explanatory example to demonstrate our design process as well as the performance improvement. The analytical results from a quasilinear model are described to offer a theoretical explanation of the system performance. This algorithm can also be applied to bandpass and MASH architectures.     

The discrete Einstein relation

In this paper the connection between massM, resistance and commute time for random walks on graphs is further explored, and the relation=2M · is proved. An extension of the result is made to multigraphs, which are an extension of the graph concept where a black box is treated like an edge.     

A Reduced Delay Method for Improving the Performance of Sigma-Delta Analog-to-Digital Converters (ADC)

Excess loop delay in a continuous-time switched-current modulator causes a stability problem and degrades the modulator's dynamic range. This paper presents a simple and effective way to reduce the loop delay and improve the modulator's performance. The loop delay of the ADC is reduced by feeding the predicted next state to the comparator. With reduced loop delay, a larger loop gain is allowed without a stability problem, and hence, the dynamic range of the ADC is improved. A new circuit architecture to realize a second-order modulator with this method is also presented. From the simulation result, the new architecture shows a 6–10 dB improvement in dynamic range for a second-order modulator.     

Routing with multiple QoS requirements for supporting multimedia applications

Distributed multimedia applications usually require multiple QoS performance guarantees. However, in general, searching such a route in the network, to support multimedia applications, is known to be NPcomplete. In this paper, we propose a new heuristic QoS routing algorithm, called QoSR_DKS, for supporting multimedia applications in highspeed networks. QoSR_DKS is a modification of rulebased Fallback routing and Dijkstra algorithms. It can search a unicast route that would have enough network resources so that multiple QoS requirements (bandwidth, delay, and delay jitter) of the requested flow could be guaranteed. Its worst case computation time complexity is the same as that of the Dijkstra algorithm, i.e., O(V²), where V is the number of nodes in the network. Extensive simulations were done with various network sizes, upto 500 nodes networks, where each node uses Weighted Fair Queueing (WFQ) service discipline. Results show that QoSR_DKS is very efficient. It could always find the QoS satisfying route, whenever there exists one (success rate is optimal), and its average computation time is near to simple shortest path Dijkstra algorithm.     

Linear phase FIR approximation of magnitude response |1/ω| for maximal flatness at an arbitrary frequency ω0, 0<ω0<π*

In many signal processing situations, the desired (ideal) magnitude response of the filter is a rational function: (a digital integrator). The requirements of a linear phase response and guaranteed stable performance limit the design to a finite impulse response (FIR) structure. In many applications we require the FIR filter to yield a highly accurate magnitude response for a narrow band of frequencies with maximal flatness at an arbitrary frequency ₀ in the spectrum (0, ). No techniques for meeting such requirements with respect to approximation of are known in the literature. This paper suggests a design by which the linear phase magnitude response can be approximated by an FIR configuration giving a maximally flat (in the Butterworth sense) response at an arbitrary frequency ₀, 0<₀<^*. A technique to compute exact weights for the design has also been given.     

Current Operational Amplifier (COA): CMOS Realization and Active Compensation

A methodology for analysis and synthesis of lowpass sigma-delta () converters is presented in this paper. This method permits the synthesis of modulators employing continuous-time filters from discrete-time topologies. The analysis method is based on the discretization of a continuous-time model and using a discrete simulator, which is more efficient than an analog simulator. In our analysis approach, the influence of the sample and hold block and non-idealities of the feedback DAC can be systematically modeled by discrete-time systems. Finally, a realistic design of a second-order modulator with a compensation of the non-ideal behavior of the DAC is given. Moreover, simulation results show a good agreement with the theoretical predictions.     

Surface-Photovoltage Measurement of Volume Electron Lifetime in p-Si Wafers

The problem of estimating the volume lifetime _v of minority carriers in p-type Si wafers by surface-photovoltage measurements is addressed. An experiment is conducted in order to ascertain the relationship between measured and actual values of _v. The measurements are carried out on circular specimens whose thickness is reduced from about 2000 to 450 m by stepwise etching. The specimens are cut from a Czochralski-grown rod, their actual values of _v ranging from 10 to 300 s. The surface recombination rate of minority carriers is determined on both sides of the specimens covered with native oxide, the sides differing in surface finish. The results of the experiment allow one to determine _v up to about 400 s.     

A 70-MHz Continuous-Time CMOS Band-Pass ΣΔ Modulator for GSM Receivers

A 70-MHz continuous-time CMOS band-pass modulator for GSM receivers is presented. Impulse-invariant-transformation is used to transform a discrete-time loop-filter transfer function into continuous-time. The continuous-time loop-filter is implemented using a transconductor-capacitor (G _m -C) filter. A latched-type comparator and a true-single-phase-clock (TSPC) D flip-flop are used as the quantizer of the modulator. Implemented in a MOSIS HP 0.5-m CMOS technology, the chip area is 857 m × 420 m, and the total power consumption is 39 mW. At a supply voltage of 2.5 V, the maximum SNDR is measured to be 42 dB, which corresponds to a resolution of 7 bits.     

Editorial

Future integrated microsystems will benefit significantlyfrom progress in the VLSI field. Two key elements will boostthe implementation of new micro-integrated architectures: progressin batch-manufactured silicon sensors and the introduction ofnew circuit techniques for designing interface circuits. Thesetwo factors will be essential in favoring the transition fromthe present research driven speculations to customer drivenactivities. This paper discusses the key issues in realizingmicrosensors and the most suitable circuit techniques for interfacingand processing their output signals. A number of examples ofintegrated structures will illustrate present problems and possiblesolutions.     

Performance of a joint CDMA/PRMA protocol with heavy‐tailed ON/OFF source

The performance of a joint CDMA/PRMA protocol with heavy-tailed ON/OFF source has been studied. Compared with the random access scheme, the PRMA protocol improves the system performance (such as packet loss, throughput) whether the traffic is SRD or LRD. The less bursty traffic is, the greater the improvement. The buffer design should take into account knowledge about the network traffic such as the presence or absence of the Noah effect in a typical source, especially of _on, the intensity of the Noah effect of ONperiod. The smaller _on is, the smaller the buffering gain, and the more packets will be lost. LRD has impacts on the overall system performance. The Noah effect, especially _off, the intensity of the Noah effect of OFFperiod, has significant impact on the overall system performance such as capacity, time delay, etc. As _off gets closer to 1, the traffic becomes more bursty, the system capacity is decreased and time delay is increased.