Delay-dependent stability criteria for linear systems with multiple time-varying delays

This paper is concerned with the delay-dependent stability analysis of a class of linear system with multiple time-varying delays. By using appropriate Lyapunov-Krasovskii functional and integral inequality lemmas, a simple delay-dependent stability criterion is proposed in LMI framework to estimate the maximum allowable bound/range of the time-delay within which the system under consideration remains asymptotically stable. The simplicity of the criterion stems from the fact that neither any terms are ignored in the analysis while dealing with the cross product terms, nor any free-weighting matrices are introduced in the theoretical derivation to counter them. Hence the resulting LMI (stability criterion) has no additional matrix variables apart from those used in the Lyapunov-Krasovskii functional. This, in turn, makes the proposed approach less conservative as well as computationally attractive. To validate the effectiveness of the proposed stability criterion, the systems considered are (i) a networked control system with dynamic output and static state feedback, and (ii) a multiple delay system with two time-varying delays.