Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

Abstract

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay

“…However, there has been less research on quadratic discrete‐time systems. In , the method of Lyapunov functions is used to study the local stability problem of nonlinear autonomous quadratic discrete‐time systems in the critical case, where the case that the spectral radius of a linearized model around the equilibrium point is equivalent to one is considered. In , the control design problem with a guaranteed stability domain for local stabilization of quadratic discrete‐time systems is investigated by using the so‐called Finsler's lemma.…”

New sufficient conditions for the asymptotic stability of discrete time-delay systems

“…A switched system with time-delay individual subsystems is called a switched time-delay system; in particular, when the subsystems are linear, it is then called a switched time-delay linear system. During the last decades, the stability analysis of switched linear continuous/discrete time-delay systems has attracted a lot of attention [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and linear matrix inequlity (LMI) approach for constructing a common Lyapunov function [19][20][21][22][23][24].…”