Static anti-windup compensator design for locally Lipschitz systems under input and output delays

Abstract

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints.