Stability analysis of nonlinear fuzzy hybrid control systems subject to saturation and delays via step-function method

Within the framework of the step-function method, the stability of a nonlinear fuzzy hybrid control system that incorporates both 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 been given scant attention, if any, in the existing studies. A new assumption is introduced in this article, thereby enabling the use of generalized sector conditions to tackle the double saturation, and the conservatism inherent in stability results is remarkably reduced owing to the improved step-function approach employed. The stability theorem proposed in this article removes constraints imposed on the time delays of both controllers, which can be also applied to wider scopes of systems, encompassing 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 the proposed theorems. © 2023 John Wiley & Sons Ltd.