Delayed state feedback predictive control of uncertain nonlinear discrete‐time switched systems with input constraint and state delays

Abstract

This study addresses the robust predictive control of a class of discrete-time switched systems under arbitrary switching signals. The subsystems of the considered switched system involve polytopic uncertainties, the state delay, non-linear terms, and input constraint. The main goal is to provide two switched delayed state feedback controllers for the cases of known and unknown state delays based on a constrained robust model predictive control method. An appropriate Lyapunov–Krasovskii functional is used to design the controller via an optimisation problem developed as linear matrix inequalities (LMIs). Both approaches are delay dependent because the online LMIs depend on the value of state delay in the first case and the upper bound of the state delay in the second one. The other advantages of the proposed method are considering a non-constrained switching signal, its ability to handle constraints, and shaping a transient response. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results and also to compare the results with previous researches.