The Novel Stability Criteria for Piecewise Affine Systems with Time-Varying Delay

Abstract

This article aims to derive new sufficient conditions to guarantee the stability of piecewise affine systems with time-varying delay (PWA-TVD). The set of delay-dependent linear matrix inequality (LMI) describes the novel stability criteria. This approach considers the PWA-TVD system with a time-delayed state-dependent switching signal. The newly suggested Lyapunov-Krasovskii functional (L-K-F) and improved estimation of its derivative have a crucial role in decreasing the complexity and conservatism of the proposed stability results. The suggested L-K-F belongs to the current and time-delayed states, the integral of the states over the time-varying delay, and time derivation of the states. A new inequality was used to obtain an upper bound (UB) for the time derivation of the Lyapunov functional. Then based on this UB, less conservative results are achieved. The theoretical results are applied to the numerical examples. The results confirm the effectiveness of the presented method. The conservative index is the maximum admissible UB of time delay.