Delay-Dependent Robust Stabilizability of Singular Linear Systems with Delays

Abstract

This article deals with the class of continuous-time singular uncertain linear systems with time-varying delay in the state vector. The uncertainties we are considering are of norm bounded type. Delay-dependent sufficient conditions on robust stability and robust stabilizability are developed. A design algorithm for a memoryless state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse-free, and robust stable is proposed in terms of the solutions to linear matrix inequalities (LMIs).

A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

“…Recently, increasing attention has been devoted to the problem of delay-dependent stability of linear systems with time-varying delay, including continuous-time and discrete-time systems with timevarying delay, and a great number of delay-dependent stability criteria were derived based on the Lyapunov functional method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. To reduce the conservativeness of the existing results, some 1494 D. YUE, E. TIAN AND Y. ZHANG new analysis methods were proposed, such as descriptor system transformation method [3,4,17], free weighting matrix method [5,8,16], matrix inequality method [9,11,18] and input-output approach [19], some of which were firstly given for continuous-time systems [3, 7-9, 11, 16], and then extended to the discrete-time systems [5,20,21].…”

Absolute stability and stabilization for Lurie networked control systems

“…Recently, delay-dependent stability for non-networked control systems with delay have attracted much attention and numerous results have been derived [11][12][13][14][15][16][17][18]. Among them, a free-weighting matrix approach [18] is reported to cover the results using Moon et al's inequality [19] and the descriptor system approach [12] becomes one of the most effective methods in dealing with the delay-dependent problem, see e.g.…”

A Stability Criterion for Singular Systems with Two Additive Time- varying Delay Components

“…Definition 2 [12,13] . The singular time-delay system (3) is said to be regular and impulse free if the pair (E, A) is regular and impulse free.…”

“…It should be pointed that the stability problem for singular systems is much more complicated than that for regular systems because not only stability but also regularity and absence of impulses (for continuous singular systems) [12−17] or causality (for discrete singular systems) [18] should be considered. Note that the stability results mentioned in [12][13][14][15][16][17][18] can only provide stability conditions for singular systems with a single delay in state. However, to the best of our knowledge, stability conditions for singular systems with multiple delay components are few even non-existing in the published works, which has motivated this paper.…”