Novel results on observer-based control of one-sided Lipschitz systems under input saturation

Abstract

This paper addresses the design of an observer-based control system for the one-sided Lipschitz (OSL) nonlinear systems under input saturation. A nonlinear matrix inequality-based control law for the nonlinear systems under input saturation and unavailable states is derived to ensure convergence of the state vector to the origin. A decoupling approach is provided for attaining simple design constraints for computing the controller and observer gains through a cone complementary linearization algorithm. In contrast to the conventional decoupling methods, the proposed approach considers OSL nonlinearity and saturation function to demonstrate both the necessity and sufficiency of the decoupled design constraints for the nonlinear matrix inequality-based main condition. To the best of our knowledge, observer-based stabilization of OSL systems under input saturation has been addressed for the first time. Novel results for the observer-based control of input-constrained Lipschitz nonlinear systems are provided as specific scenarios of the proposed results. Simulation results of the proposed control scheme to a flexible-joint robot and a complex nonlinear circuit are presented.