Predictive Control Design for Discrete Switched Affine Systems Subject to a Constant Input Delay

This contribution presents the stabilization of switched affine systems subject to an input delay in the switching signal. The proposed approach extends an existing control Lyapunov function method, which guarantees the stabilization to an a priori defined limit cycle in the case of a constant input delay. The main contribution relies on the definition of an augmented system, which includes the past values of the control input and on predictor, which is considered in the min-switching state-feedback control. As a result, a stabilization condition expressed as a delay-independent LMI ensures that the trajectories of the closed-loop system converge to a limit cycle. A numerical application validates the obtained results and highlights some perspectives.