Finite-time stability of discrete-time systems with time-varying delay

Abstract

Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, finite-time stability problem for a class of linear time-varying delay systems is studied. Based on Lyapunov-like functions method and using an appropriate model transformation of the original system, the sufficient delay-dependent finite-time stability conditions are derived. The criteria are presented in the form of LMIs, which are dependent on the minimum and maximum delay bounds. The numerical examples are presented to illustrate the applicability of the developed results

Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional

“…In the existing literature, there are two concepts of finite-time stability (FTS) with a very different meaning. The first concept of FTS requires that the state of system does not exceed a specified bound in a given finite-time interval [14][15][16][17][18][19][20][21][22][23][24][25][26][27], while in the second concept the term FTS is used to describe system whose state approaches equilibrium point in a finite time [27,28]. In our paper, the first concept of FTS is considered.…”

“…Some results on FTS can be found in [17][18][19][20] for singular systems and [21][22][23][24][25] for singular time-delay systems. Paper [21] presents an overview of existing results in the field of FTS and gives new sufficient conditions.…”

“…In reference [24], in the process of majoritarian of LLF an integral term with delayed states is omitted. The problem FTS of the singular discrete-time systems is studied in [25,26].…”

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

“…[7], FTS analysis and control problems were discussed for many kinds of linear systems. Recently, due to the importance in the study of the transient behavior of systems, FTS has been introduced into many different fields, such as nonlinear systems [8,9], stochastic systems [10,11], singular systems [12][13][14], time-delay systems [15,16], fractional order systems [17], and switched systems [18][19][20], and many related results have been obtained.…”

Finite-Time Stability of Continuous Time Delay Systems: Lyapunov-like Approach with Jensen’s and Coppel’s Inequality

“…These results are conservative, because they use the inequalities based on the norm of state vector. Recently, using new boundary technique based on the vector and matrix inequality, integral or no integral type, some less conservative results are obtained [19][20][21][22].…”