Robust Admissibility of Uncertain Singular Nonlinear Time-Delay Systems Based on Nonlinear Memory Feedback Control

Based on nonlinear memory feedback, the robust admissibility problem of a class of singular nonlinear time-delay systems was investigated. First, an equivalent structural model of the system was created using the state decomposition approach. Then, sufficient criteria for the robust admissibility of the system were obtained in the form of linear matrix inequalities using the Lyapunov–Krasovskii theory and free weighted matrix method. Subsequently, the closed-loop robust admissibility of the system under nonlinear memory feedback control was investigated using similar research techniques as before, yielding corresponding results. The intended design controller was obtained by explicitly computing each component in the deconstructed structure of the nonlinear memory feedback controller. Importantly, the flexibility and viability of the planned control design could be enhanced by the algorithm for solving controller gain through this component decomposition. Finally, numerical examples confirmed the feasibility of the method.