Exponential stability criteria for discrete time‐delay systems

Abstract

SUMMARYIn this paper, we study the exponential stability of linear discrete time-delay systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in Hilbert spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. As an application of the main results, we discuss the exponential stability of a general nonlinear system. The main novelty of this work is that we always consider the exponential behavior of solutions with respect to an specific ball.

Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay

“…Although time delay usually causes undesirable dynamic behaviors such as performance degradation or even instability, its introduction can also enhance performance or stabilize systems in some cases [1]. Therefore, the problem of stability analysis for systems with time-varying delay is very meaningful in both theory and practice [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems

“…Furthermore, for a fixed feasible solution of (17), any solution of system (1) has the exponential convergence estimate (19) below.…”

“…Recently, by associating the second Lyapunov method and the Lyapunov matrix equation approach, sufficient conditions for exponential stability and explicit exponential estimates of solutions of system are derived in , which generalizes the result obtained in . Furthermore, the results obtained in were extended to the perturbed LDDSs in , and to the time‐varying LDDSs in .…”

“…The linear delay difference systems (LDDSs) are very important in the compute simulations of the continuous-time systems. Therefore, the stability analysis of LDDSs has received extensive attention in the past two decades (see [14][15][16][17][18][19][20] and the references therein).…”