Stability analysis of uncertain systems with time-varying delays via simplified Lyapunov-Krasovskii functionals

Abstract

Uncertainties and time delays exist in practical control systems, which often lead to instability or performance degradation. The existing stability conditions for delay systems are mainly divided into two categories: delay-independent conditions and delay-dependent ones. In general, delay-dependent conditions are less conservative than those of delay-independent ones. In order to reduce conservativeness of these results, many researchers have made unremitting efforts. In particular, with improved Lyapunov-Krasovskii functionals, together with linear matrix inequalities (LMI) approach, we study robust stability of time-varying delay systems with parametric uncertainties. In this paper we first re-visit some delay-dependent LMI stability criteria. Then the stability analysis process is made more concise by simplifying Lyapunov-Krasovskii functionals, which can be graded more easily, and thus results in stability conditions of less conservativeness. Finally, using the single-machine-infinite-bus system as application, we illustrate upper bounds of time delay in the system that are allowable for the system to be robustly stable. Numeric simulation verifies validity of the suggested methods.