Separation principle of perturbed time-varying systems with periodic nominal part

Abstract The purpose of this paper is to provide a comprehensive view of the theory of separation principle for a class of perturbed time-varying systems with periodic nominal parts. The contributions are as follows. First, based on the Lyapunov function techniques and Floquet theory, the practical stabilization of the closed-loop systems is achieved. Second, we propose a practical observer to estimate the system states. Necessary and sufficient assumptions are provided to prove the practical stability of the proposed observer. These results demonstrate that a separation principle for perturbed time-varying systems with periodic nominal parts can be obtained. Finally, simulation results were shown to illustrate the feasibility of the proposed strategy.