Non-fragile control of periodic piecewise linear time-varying systems with time delay

Abstract

In this study, the stability and stabilisation issues of a class of periodic piecewise linear time-varying systems with time delay are studied. Based on a lemma with respects to the negative definite matrix polynomial, a sufficient delay-dependent exponential stability condition is obtained via constructing a Lyapunov–Krasovskii functional with periodic matrix functions. Then, for two types of norm-bounded uncertainties of time-varying controller gains, the non-fragile stabilising controllers under the multiplicative and additive gain perturbations are designed to stabilise the closed-loop system. The obtained controller gains could be solved with linear matrix inequalities directly instead of using the iterative algorithm. That is valued in engineering applications. Numerical examples are presented to demonstrate the effectiveness of the proposed methods.