Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

Abstract

This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

Stability analysis for singular random impulsive control system: A novel neutral impulsive delay system approach

“…Therefore, for uncertain STDSs, the investigation of robust stability is imperative. Exploring the literature, some recent results on robust stability results have been documented in previous papers [5–14].…”

“…of robust stability is imperative. Exploring the literature, some recent results on robust stability results have been documented in previous papers [5][6][7][8][9][10][11][12][13][14].…”

Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

“…As we all know, it is required to consider not only stability but also regularity and absence of impulses (for continuous singular systems) or causality (for discrete singular systems) simultaneously for singular systems; thus, the study on singular systems is much more complicated than that on the regular ones [3,4]. Recently, many scholars have applied themselves to the research of singular system and many stability and stabilization conditions have been established for singular systems; see, for example, [5][6][7][8][9][10][11] and the references therein.…”