Constrained Robust Predictive Control of Discrete Switched Systems With Time Delay: Static and Dynamic Output Feedback Controllers

ABSTRACT This paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.