Abstract

Under the framework of the step-function method, the stability of a nonlinear fuzzy hybrid control system combining an impulsive controller and a continuous state feedback controller is investigated. Both the two controllers are assumed to be subject to both actuator saturation and time-varying delays, which has received little attention if any, in the existing studies. A new assumption is established enabling the use of generalized sector conditions to tackle the double saturation, and the conservatism of the stability results is remarkably reduced thanks to the improved step-function method. The stability theorem proposed in this paper removes restriction on the time delays of both controllers, which can be also applied to wider scopes of systems, including hybrid control systems with both stabilizing and instabilizing impulses, systems with varying impulsive gain, and systems with Zeno behavior. Numerical simulations of stabilization for different systems by delayed saturated hybrid control have been conducted, which demonstrate the validity of proposed theorems.