Robust stability for a class of two-time-scale time-delay neutral systems

In this paper the H/sub /spl infin//-optimal control and risk-sensitive control of linear singularly perturbed, discrete-time systems are considered. It is shown that the Riccati equation associated with the solution of the H/sub /spl infin//-optimal control problem, can be approximated by an outer series solution, and a boundary-layer correction series solution. As the singular perturbation parameter /spl epsiv/ tends to zero, it is shown that the full-order Riccati equation can be approximated by the zeroth-order outer-series solution. It is also recognized that the outer-series solution and the boundary-layer solution, are equivalent to the resulting asymptotic series expansion in powers of /spl epsiv/, of the Riccati equation associated with a certain risk-sensitive control problem. When a two-time-scale decomposition is considered, it is shown that an approximate composite control can be formed, as the sum of the slow and fast subsystems. Unlike the asymptotic expansion approach, it is shown that the original system can be approximated by the maximum of the performance associated with the slow and fast subsystems. Finally, it is shown that the slow and fast subsystems, are equivalent to certain slow and fast subsystems, respectively, resulting from applying a two-time-scale decomposition to a certain risk-sensitive control problem. >

This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet. Suppose that for each n /spl ges/ 1 X/sup n/ is encoded to a binary codeword /spl phi//sub n/(X/sup n/) of length l(/spl phi//sub n/(X/sup n/)). Letting /spl epsiv//sub n/ denote the decoding error probability, we consider the following two criteria on FV codes: i) /spl epsiv//sub n/ = 0 for all n /spl ges/ 1 and ii) lim sup/sub n/spl rarr//spl infin///spl epsiv//sub n/ /spl les/ /spl epsiv/ for an arbitrarily given /spl epsiv/ /spl isin/ [0,1). Under criterion i), we show that, if X/sup n/ is encoded by an arbitrary prefix-free FV code asymptotically achieving the entropy, 1/nl(/spl phi//sub n/(X/sup n/)) - 1/nlog/sub 2/ 1/PX/sup n/(X/sup n/) /spl rarr/ 0 in probability as n /spl rarr/ /spl infin/ under a certain condition, where P/sub X//sup n/ denotes the probability distribution of X/sup n/. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/nl(/spl phi//sub n/(X/sup n/)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.

This paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems. The first one is an /spl epsi/-dependent controller that stabilizes the closed-loop system for all /spl epsi//spl isin/(0, /spl epsi//sub 0/*), where /spl epsi//sub 0/* is the prespecified upper bound of the singular perturbation parameter. The second one is an /spl epsi/-independent controller, which is able to stabilize the system in the entire state space for all /spl epsi//spl isin/(0, /spl epsi/*), where /spl epsi/* is the exact upper /spl epsi/-bound. The /spl epsi/* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes.

This paper investigates the robust stability for a class of uncertain neutral system with time-varying delay and nonlinear uncertainties. A new delay-dependent stability criteria is presented by using Lyapunov method. The stability criteria for such systems in terms of linear matrix inequalities (LMIS). Some numerical examples show that the effectiveness and the significantly important over some existing results.

This paper investigates the problem of robust delay-dependent stability analysis of uncertain neutral delay systems. Based on a new approach which suggests very closed lower bound of Jensen's inequality by the use of Wirtinger inequality, an extended inequality is proposed. Moreover, by considering norm bounded uncertainties in system matrices, a robust stability criterion of uncertain neutral delay systems is studied. Two numerical examples are given to describe the less conservatism of the proposed methods.

Presents an algorithm for minimizing the search effort of a mobile robot navigating in an unknown environment. First we describe a strategy for navigating a cylinder-shaped mobile robot in an area with unknown obstacles using range data. The strategy searches a graph which is constructed incrementally during the navigation process. Then we present a new algorithm for searching the graph which attempts to minimize the search effort, measured by the length of the path traveled by the robot. The algorithm, called A/sub /spl epsiv//*-DFS, combines features of the classical A* and DFS graph-search algorithms, and generates /spl epsiv/-optimal paths. Moreover, A/sub /spl epsiv//*-DFS is general and can be used by any online search strategy. The algorithm uses E as a parameter, where /spl epsiv/=0 corresponds to A* while /spl epsiv/=/spl infin/ corresponds to DFS. We study the performance of A/sub /spl epsiv//*-DFS for various values of /spl epsiv/ on simulated environments, and indicate how to best choose /spl epsiv/ for a given class of environments.

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties

According to the Lyapunov stability theorem and the bounds of solutions of the Lyapunov equation, the state feedback gain matrices can be determined to guarantee the stability of the singularly perturbed systems for all /spl epsiv//spl isin/(0,/spl infin/). A numeral example and an operational amplifier circuit are given to illustrate the effectiveness of the proposed scheme.

Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay

This paper deals with the problem of robust stability of uncertain neutral type singular system with neutral and discrete delays. By employing a new integral inequality, a delay-dependent robust stability criterion is obtained in the form of linear matrix inequality(LMI). Numerical examples illustrate the effectiveness of this approach and the improvement over previous methods.

Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

This paper focuses on the robust stability and the memory feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Especially, the considered time delays depend on the subsystem number. Based on a novel common Lyapunov functional, the aggregation techniques, and the Borne and Gentina criterion, new sufficient robust stability and stabilization conditions under arbitrary switching are established. Compared with existing results, the proposed criteria are explicit, simple to use, and obtained without finding a common Lyapunov function for all subsystems through linear matrix inequalities, considered very difficult in this situation. Moreover, compared with the memoryless one, the developed controller guarantees the robust stability of the corresponding closed-loop system with more performance by minimizing the effect of the delays in the system dynamics. Finally, two numerical simulation examples are shown to prove the practical utility and the effectiveness of the proposed theories.

The asymptotic behavior of the /spl epsiv/-entropy of ellipsoids in an n-dimensional Hamming space whose coefficients take only two different values is investigated as n /spl rarr/ /spl infin/. Explicit expressions for the main terms of the asymptotic representation for the /spl epsiv/-entropy of such ellipsoids are obtained under different relations between /spl epsiv/ and parameters defining these ellipsoids.