Stability Analysis Of Discrete-time Systems Research Articles

Delay-dependent stability analysis for discrete-time systems with time varying state delay

The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results.

The Delay-Dependent for Discrete-Time Systems

Problem statement: This study is concerned with the problem of delay- dependent stability analysis for discrete-time systems with interval-li ke time-varying delays. Conclusion/Recommendations: The problem is solved by applying a novel Lyapunov functional and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. into account. It is worth noting that the closed-lo op system resulting from a delayed controller is actua lly a time-delay system. Therefore, stability results o f time-delay systems could be applied to design time- delayed controller. The present study a new Lyapunov functional, an improved delay-dependent stability criterion for discrete-time systems with time-varying delays is presented in terms of LMIs. It is shown that the obtained result is less conservative than those in. Example is providing, respectively, to demonstrate the reduced conservatism of the proposed stability crit erion and the effectiveness of the proposed design method . Preliminaries: Lemma 2.1 (Agarwal, 2000) the zero solution of difference system is asymptotic stabili ty if there exists a positive definite function n

Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay

This study focuses on studying the asymptotical stability analysis problem for discrete-time systems with time-varying delay. By utilising the S-procedure and an inequality technique, a novel delay-dependent stability criterion is derived in terms of two linear matrix inequalities. Since no slack variable is introduced, less decision variables are involved in the stability condition and the burden of numerical computation is thus reduced. It is also rigorously proved that the authors' result is less conservative than some recent ones. Furthermore, the developed approach is extended to address the stability analysis problem of delayed discrete-time systems with norm-bounded uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

Stability analysis of discrete-time systems with additive time-varying delays

In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has practical application background in networked control systems. The stability criterion is expressed in the form of linear matrix inequalities (LMIs), which can be readily solved by using standard numerical software. An illustrative example is provided to show the advantage of the proposed stability condition.

Stability Criterion for Discrete-Time Systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.

A delay-partitioning approach to the stability analysis of discrete-time systems

This paper revisits the problem of stability analysis for linear discrete-time systems with time-varying delay in the state. By utilizing the delay partitioning idea, new stability criteria are proposed in terms of linear matrix inequalities (LMIs). These conditions are developed based on a novel Lyapunov functional. In addition to delay dependence, the obtained conditions are also dependent on the partitioning size. We have also established that the conservatism of the conditions is a non-increasing function of the number of partitions. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.

Noncausal linear periodically time-varying scaling for robust stability analysis of discrete-time systems: Frequency-dependent scaling induced by static separators

This article is concerned with robust stability analysis of discrete-time systems and introduces a novel and powerful technique that we call noncausal linear periodically time-varying (LPTV) scaling. Based on the discrete-time lifting together with the conventional but general scaling approach, we are led to the notion of noncausal LPTV scaling for LPTV systems, and its effectiveness is demonstrated with a numerical example. To separate the effect of noncausal and LPTV characteristics of noncausal LPTV scaling to see which is a more important source leading to the effectiveness, we then consider the case of LTI systems as a special case. Then, we show that even static noncausal LPTV scaling has an ability of inducing frequency-dependent scaling when viewed in the context of the conventional LTI scaling, while causal LPTV scaling fails to do so. It is further discussed that the effectiveness of noncausal characteristics leading to the frequency-domain interpretation can be exploited even for LPTV systems by considering the ν N -lifted transfer matrices of N -periodic systems.

Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

New Results on Stability of Discrete-Time Systems With Time-Varying State Delay

This note is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence, several new conditions are obtained for the asymptotic stability of these systems. The merit of the proposed conditions lies in their less conservativeness, which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms Sigmam=k-dk k-1(middot) and Sigma m=k-dM k-1(middot), which is largely ignored in the existing literature. These conditions are shown, via several examples, to be much less conservative than some existing result

NONCAUSAL LINEAR PERIODICALLY TIME-VARYING SCALING FOR DISCRETE-TIME SYSTEMS

This paper is concerned with robust stability analysis of discrete-time systems. We first consider linear periodically time-varying (LPTV) nominal systems, for which we apply the discrete-time lifting to have their equivalent linear time-invariant (LTI) representations. Applying the conventional but general scaling approach to the LTI representations leads to the notion of noncausal LPTV scaling when the scaling is interpreted in the original time axis without lifting. Regarding this discrete-time noncausal LPTV scaling, we confirm its effectiveness over causal LPTV scaling and (causal) LTI scaling theoretically as well as with a numerical example. We next consider LTI nominal systems, for which we again apply noncausal LPTV scaling by regarding the LTI systems as a special case of LPTV systems and thus applying the discrete-time lifting in the same way as in the LPTV nominal systems. We then study the relationship of such an approach with the conventional LTI scaling applied directly to the LTI nominal systems without lifting treatment. In particular, we show that even static noncausal LPTV scaling yields dynamic (frequency-dependent) LTI scaling if it is interpreted in the context of lifting-free treatment, and an advantage of noncausal LPTV scaling for LTI nominal systems is investigated from this viewpoint. A numerical example is also provided that supports the advantage.

Absolute stability analysis of discrete-time systems with composite quadratic Lyapunov functions

A generalized sector bounded by piecewise linear functions was introduced in a previous paper for the purpose of reducing conservatism in absolute stability analysis of systems with nonlinearity and/or uncertainty. This paper will further enhance absolute stability analysis by using the composite quadratic Lyapunov function whose level set is the convex hull of a family of ellipsoids. The absolute stability analysis will be approached by characterizing absolutely contractively invariant (ACI) level sets of the composite quadratic Lyapunov functions. This objective will be achieved through three steps. The first step transforms the problem of absolute stability analysis into one of stability analysis for an array of saturated linear systems. The second step establishes stability conditions for linear difference inclusions and then for saturated linear systems. The third step assembles all the conditions of stability for an array of saturated linear systems into a condition of absolute stability. Based on the conditions for absolute stability, optimization problems are formulated for the estimation of the stability region. Numerical examples demonstrate that stability analysis results based on composite quadratic Lyapunov functions improve significantly on what can be achieved with quadratic Lyapunov functions.

Stability analysis of discrete-time systems in a state-space realisation with state saturation nonlinearities: linear matrix inequality approach

A computationally efficient linear matrix inequality (LMI)-based criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with state saturation nonlinearities is presented. The criterion turns out to be an improved generalised version of a previously reported LMI-based criterion. The extension of the approach to a situation involving partial state saturation nonlinearities is performed.

Stability of Markov modulated discrete-time dynamic systems

Motivated by various control applications, this paper develops stability analysis of discrete-time systems with regime switching, in which the dynamics are modulated by Markov chains with two time scales. Using the high contrast of the different transition rates among the Markovian states, singularly perturbed Markov chains are used in the formulations. Taking into consideration of the regime changes and time-scale separation makes the stability analysis a difficult task. In this work, asymptotic stability analysis is carried out using perturbed Liapunov function techniques. It is demonstrated that if the limit system is stable, then the original system is also stable. In addition, we examine path excursion, derive bounds on mean recurrence time, and obtain the associated probability bounds.

Stability analysis of discrete-time systems in a state-space realisation with partial state saturation nonlinearities

A criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with partial state saturation nonlinearities is presented. The criterion is compared with a previously reported criterion.

Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.

Robust stability analysis of discrete-time systems using genetic algorithms

We reduce stability robustness analysis for linear, time-invariant, discrete-time systems to a search problem and attack the problem using genetic algorithms. We describe the problem framework and the modifications that needed to be made to the canonical genetic algorithm for successful application to robustness analysis. Our results show that genetic algorithms can successfully test a sufficient condition for instability in uncertain linear systems with nonlinear polynomial structures. Three illustrative examples demonstrate the new approach.