Constrained Model Predictive Stabilizer of Nonlinear Discrete‐Time Switched Systems With Parametric Uncertainty and Time‐Varying Delay

ABSTRACT This article presents a framework to control discrete‐time switched systems under the challenges of time‐varying delays, parametric uncertainties, arbitrary switching conditions, and unknown nonlinear Lipschitz terms. Additionally, constraints on both control inputs and state variables are considered. The proposed controllers are developed using the constrained robust model predictive control (RMPC) strategy, employing both online and offline approaches. These controllers are implemented as delayed state feedback strategies, applicable to scenarios with either known or unknown time delays. The corresponding optimization problem is derived based on a well‐designed Lyapunov–Krasovskii functional. Utilizing the Switched Lyapunov Function (SLF) methodology, the problem is reformulated as a feasibility analysis of a set of linear matrix inequalities (LMIs), ensuring the asymptotic stability of the closed‐loop system. Other key features of the proposed approach include enhanced transient performance, effective handling of system constraints, and compatibility with arbitrary switching signals. The theoretical results are validated through numerical simulations, demonstrating the method's effectiveness and comparing its performance against existing techniques.