Aperiodic Sampled-Data Stabilization of Switched Systems Via an Extended Looped-Functional Approach

This technical note is concerned with the stabilization of continuous-time switched linear systems under aperiodic sampled-data control. An extended looped-functional framework is developed by introducing a novel piecewise Lyapunov functional that explicitly incorporates sampled switching information. Based on this construction, sufficient asymptotic stability conditions are derived in terms of Metzler-matrix inequalities, enabling the joint design of state-dependent switching laws and state-feedback controllers. Unlike existing approaches, the proposed method can ensure stability even when all subsystems are unstable or uncontrollable, including the limiting case where no control input is available and switching acts as the sole stabilizing mechanism. The resulting sampled switching strategy inherently enforces a minimum dwell time determined by the sampling interval, avoids chattering, and allows direct computation of admissible aperiodic sampling bounds. The framework is also applicable to systems with parametric uncertainties. Numerical examples illustrate the reduced conservatism and effectiveness of the proposed approach.