Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti-windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous L₂ bounded input. The system is presumed to have locally Lipschitz nonlinearities, time-varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm-bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter-varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and L₂ gain minimization. The proposed multiobjective AWC-based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time-varying parametric norm-bounded uncertainties, the asymptotic stability of the closed-loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC-based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.