Finite‐time boundedness and control design of uncertain switched systems with time‐varying delay under new switching rules

Abstract In this article, the finite‐time boundedness and control problem for time‐delay switched systems with uncertainties are studied. The delay is considered as time‐varying delay rather than constant delay, which is more suitable for practical engineering. First, the property of finite time boundedness for uncertain switched system without control input is researched by constructing a proper Lyapunov–Krasovskii functional (LKF) with three integral terms and the minimum LKF switching rules. Then, a state feedback controller with switching is designed. By utilizing Finsler's Lemma and singular value decomposition (SVD), sufficient conditions for finite‐time boundedness of time‐delay switched systems with control input and controller gain are presented. Additionally, a filter system is designed. The finite time boundedness and filter parameters of the closed‐loop error system are obtained by using the auxiliary matrix method. Finally, the feasibility of the proposed methods and the significance of switching rule are demonstrated through two numerical examples.