The guaranteed cost controller for nonlinear systems with time-varying parameters and input saturation

Abstract

This paper investigates the uniformly asymptotically/exponentially stable guaranteed cost control problem for a class of nonlinear systems with time-varying parameters and input saturation. The nonlinearities and the time-varying nature of these systems render it quite challenging to solve the guaranteed cost control problem. This paper presents a new Lyapunov functional and a novel controller structure as nonlinear and parameter-varying forms incorporating the state, the time-varying parameters and its derivative. Based on Lyapunov stability theory, the solvable conditions for the existence of guaranteed cost controllers are obtained in terms of state-and-parameter-dependent linear matrix inequalities, which can be efficiently solved via sum-of-squares convex programming. Finally, the effectiveness of the proposed method is demonstrated by the conversion flight control of a tilt rotor aircraft.