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

Abstract

Abstract:The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities (LMIs). Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.

Delay-Dependent Stability Criteria for Continuous Systems with Two Additive Interval Time-Varying Delays and Nonlinear Perturbations

“…[11][12][13][14][15][16][17][18][19]). It is worth pointing out that there has a technical problem in the Theorem 3.1 and proof in [17] (see [20]).…”

“…Remark 3 Based on the Lyapunov functional (23), Corollary 2 proposed a new delaydependent stability criterion for system (15). It is noted that unlike the Lyapunov functionals chosen in [11][12][13][14][15][16][17][18][19], the constructed Lyapunov functional (23) takes the [11][12][13][14][15][16][17][18][19], which will be demonstrated in the sequel.…”

“…Remark 4 It is worth mentioning that in [11][12][13][14][15][16]18], too many free-weighting matrices were introduced to discuss the stability problem for system (15). However, some matrices do not reduce the conservatism of the resulting criterion, on the contrary, they make the analysis more complicated.…”

“…M . Thus, the criterion in Corollary 2 has less decision variables than the ones in [11][12][13][14][15][16]18]. …”

“…In [15], by defining a more general Lyapunov functional and employing convex polyhedron method to estimate the upper bound on the time derivative of the Lyapunov functional, an improved delaydependent stability criterion is established. In [16], by using a simple type of Lyapunov functional, some delay-dependent stability criteria for singular system with two additive time-varying delays were established with fewer matrix variables. Very recently, by taking advantage of integral inequalities and new Lyapunov functional, some new less conservative delay-dependent stability criteria are presented in [17][18][19].…”