Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

Abstract

Nonlinear discrete control system theory, which is increasingly garnering attention, has important applications in computer control theory. In this study, the robust control problem of nonlinear discrete systems with perturbations is investigated. Using the Lyapunov theory and linear matrix inequality method, the sufficient conditions for fast convergence of the state observer estimation error and fast stability of the state feedback closed-loop system are formulated, thereby showing that the independent solution of the gain matrix of the state observer and robust controller is more convenient. When designing the state observer and observer-based robust controller, the gain matrix was constrained twice, reducing the time required for robust control. The proposed robust control method based on the state observer reduces the conservatism of the system and improves the robust control effect of nonlinear discrete systems. Concurrently, the observer-based robust control method in normal systems is extended to the generalized system form. Finally, the proposed robust control method was simulated using the longitudinal motion model of an aircraft and the DOLPHIN MARK II autonomous underwater vehicle motion model, as research objects. In comparisons with two control methods from the literature, the average error of state estimation was significantly reduced, and the closed-loop control system rapidly achieved robust stabilization, demonstrating the effectiveness and superiority of the control method proposed in this paper.

Keywords

• Nonlinear system
• discrete system
• controller
• observer
• linear matrix inequality
• gain matrix