Matrix-injection-based transformation method for discrete-time systems with time-varying delay

Stability analysis of discrete‐time systems with a time‐varying delay via improved methods

“…Very recently, a matrix-injection-based transformation method was proposed to ensure the negativity of a cubic function [17] by introducing two free matrices. However, one of the matrices is high-dimensional and hence there are still a lot of decision variables involved.…”

“…On the other hand, the introduction of a time delay can make some systems stable that is originally unstable without the delay [2] and can also accelerate the rate of convergence of system states [13]. Therefore, when the delay is time-varying, it is necessary to study the maximal allowable time-varying region in which the delay varies while the system studied remains stable [14][15][16][17][18]. During the last decades, much effort has been devoted to study the following discrete-time system with a time-varying delay [19][20][21][22][23][24][25]:…”

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

“…Over the past three decades, considerable effort has been devoted to the synthesis of time-delay systems, leading to numerous research results for both continuous-time and discrete-time systems. [1][2][3][4][5][6][7][8][9][10] Understanding and analyzing the impact of delays requires the development of stability criteria. Lyapunov stability theory and linear matrix inequality (LMI) technology have been widely used in most studies concerning the stability of time-delay systems.…”

“…Time‐varying delay (TVD) is a well‐known challenge in engineering applications, often leading to poor system performance, instability, and failure to achieve desired objectives. Over the past three decades, considerable effort has been devoted to the synthesis of time‐delay systems, leading to numerous research results for both continuous‐time and discrete‐time systems 1‐10 …”

Novel stability criteria for discrete‐time delayed neural networks via extended negative‐definiteness approaches of matrix‐valued quadratic function

“…[34][35][36] that consider different negative definite quadratic function conditions. Based on these theories, the negative-definiteness lemmas for quadratic function are proposed by matrix transformation methods [37][38][39]. However, the additional decision variable introduced in previous methods is redundant, and the symmetry of matrix-valued coefficients on polynomial has not been considered, which may lead to conservatism and expensive computational complexity.…”