Guaranteed cost control of periodic piecewise linear time-delay systems

Abstract

This paper is concerned with the guaranteed cost control problem for continuous-time periodic piecewise linear systems with time delay. Sufficient delay-dependent conditions of closed-loop asymptotic stability are presented based on an improved formulation, which uses a novel Lyapunov–Krasovskii functional with relaxed requirement in positive definiteness of the involved symmetric matrices. The corresponding optimization problems aiming at the mixed performance involving an upper bound of H2 guaranteed cost and an H∞ performance index for disturbance attenuation are established. By designing an iterative algorithm subject to the proposed conditions, the periodic guaranteed cost controller gains over each sub-interval are tractable for the resulting closed-loop time-delay system. The effectiveness and reduced conservatism of our proposed criteria are validated and illustrated via numerical simulations.