Robust Finite-Time Stabilization for Uncertain Discrete-Time Linear Singular Systems

Abstract

This paper considers the robust finite-time stabilization problem for a class of discrete-time linear singular systems with norm-bounded parameter uncertainties. With the introduction of an additional matrix to describe the algebraic relationship between the slow subsystem and fast subsystem of a discretetime linear singular system, a matrix inequality condition is first given for a discrete-time linear singular system to be regular, causal and finite-time stable. With this condition, the robust finite-time stability and robust finite-time stabilization problems are also resolved, and the explicit expression of the desired state feedback control law is also given in terms of a set of matrix inequalities. A numerical example is given to show the effectiveness of the proposed method. INDEX TERMS uncertain linear singular system, discrete-time singular system, finite-time stability, finitetime stabilization, matrix inequality

Finite‐time stability of singular multi‐agent systems with input time‐varying delay and non‐linear dynamics via non‐fragile controller

“…2. In contrast to the works [17][18][19] about finite-time stability analysis of singular single systems, this paper attempts to tackle the finite-time stability issue of singular multi-agent systems by considering input time-varying delay, Lipschitz non-linear dynamics and controller gain perturbation at the same time. Therefore, this paper is closer to the practical engineering systems.…”

“…Furthermore, references [10–12] assume that the controller gain keeps constant in the actual process, which is unreasonable and unrealistic. On the contrary, this paper considers that inaccuracy exists in the execution of the controller and designs a non‐fragile distribute controller to solve the problem. In contrast to the works [17–19] about finite‐time stability analysis of singular single systems, this paper attempts to tackle the finite‐time stability issue of singular multi‐agent systems by considering input time‐varying delay, Lipschitz non‐linear dynamics and controller gain perturbation at the same time. Therefore, this paper is closer to the practical engineering systems.…”

New Approach to Observer-Based Finite-Time H∞ Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

“…Hence, the finite-time transient performance should be considered. Recently, finite-time stability and H ∞ control problems have gradually become a well-researched topic and have been applied to many systems [15][16][17][18] . In 2020, Wang J X et al [15] considered the problem of robust finite-time stabilization for uncertain discrete-time linear singular systems.…”

“…Recently, finite-time stability and H ∞ control problems have gradually become a well-researched topic and have been applied to many systems [15][16][17][18] . In 2020, Wang J X et al [15] considered the problem of robust finite-time stabilization for uncertain discrete-time linear singular systems. Feng T et al [16] studied the problem of finite time stability and stabilization for fractional-order switched singular continuous-time system.…”

l₂–l ∞ Control for Discrete-Time Descriptor Systems

“…The descriptor system [1]- [3], also known as singular system, has provided a unified and useful modeling method for many real applications, such as electricity, aerospace, and social economy. Therefore, it is clearly observed that the study on descriptor system is active over the recent decades and has made great process [4], [5], in which, as the most important field, the problem of asymptotic stability and feedback stabilization have been attracted more attention from researchers. And some results involving the research on system performance analysis for descriptor system have been reported, for instance, in [6], the problem of a reduced-order H ∞ controller based on the geometric structures was solved.…”