Finite-time H_∞ controller synthesis for almost periodic piecewise linear systems with dwell time uncertainty

In this paper, we investigate the finite-time H_∞ controller synthesis for a class of almost periodic piecewise linear systems with dwell time uncertainty, under the framework of finite-time stability and finite-time boundedness. Due to the difficulty in locating the exact switching instants under almost periodicity, a periodic piecewise finite-time controller is developed using a specifically designed Lyapunov-like function. Time-varying constraints are provided to ensure finite-time stability in both deterministic and uncertain switching intervals. Moreover, time-varying constraints based on an interpolation form can be converted into linear matrix inequalities, enabling closed-loop finite-time boundedness to be tractable via convex optimization. Similarly, the sufficient conditions for stabilizing control and H_∞ robust synthesis are obtained by decoupling the associated time-varying constraints. The effectiveness of our proposed approach is validated through an equivalent mass-spring-damper system.