Disturbance Rejection‐Based Control Design for Periodic Piecewise Polynomial Time‐Varying Systems

The aim of this study is to examine the disturbance rejection and stabilization problem for a class of periodic piecewise polynomial time‐varying systems with time‐delays, uncertainties and multiple disturbances. Specifically, the matching disturbances induced by the external systems are initially addressed by building an observer of disturbances. Meanwhile, the mixed and passivity performance handles the mismatched portion. The control law is created by combining the disturbance observer's output with a composite control rule. Precisely, periodic piecewise time‐varying systems are formed by dividing the fundamental period of periodic systems into a limited number of subintervals. Also, by combining the periodic piecewise Lyapunov–Krasovskii functional with a matrix polynomial lemma, a series of delay‐dependent adequate conditions for linear matrix inequalities is obtained. These developed conditions confirm that the system under consideration is asymptotically stable. According to these conditions, periodic gain matrices are computed for both the controller and observer. The final step in our work is to demonstrate the validity of theoretical results as well as control schemes using a numerical example.