Dwell time-based stabilisation of switched linear delay systems using clock-dependent Lyapunov-Krasovskii functionals

Abstract

Dwell time stability conditions of the switched delay systems are derived using multiple clock-dependent Lyapunov-Krasovskii functionals. The corresponding conditions are approximated by both using piecewise linear functions and sum of squares polynomials. The upper bound of the dwell time is minimised using a combination of a bisection and a golden section search algorithm. Using the results obtained in the stability case, synthesis of dwell time minimiser controllers are presented. Some numerical examples are given to illustrate effectiveness of the proposed method, and its performance is compared with the existing approaches. The resulting values of the dwell time via the proposed technique show that the novel approach outperforms the previous ones.