An improved control approach for a class of continuous-time switched system with time-varying delay

LESSI Laboratory, Faculty of Science Dhar El Mehraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco.

^* e-mail: amina.elmaach@usmba.ac.ma
^** e-mail: mohammed.charqi@usmba.ac.ma

Abstract

In this paper, an improved method is developed for designing controllers for linear switched systems with time-varying delays, focusing on the Hurwitz-convex combination framework. For this, by using a Lyapunov–Krasovskii functional, the stability analysis is carried out, and the obtained conditions are expressed in terms of Linear Matrix Inequalities (LMIs). By solving these LMIs, one can determine an upper bound on the delay that ensures the stability of the considered system. Compared to some existing results in the literature, the proposed approach yields less conservative results and allows for significantly larger admissible delay bounds. Finally, some numerical examples are provided to demonstrate the effectiveness and to improve the performance of the proposed design scheme.