Novel stability analysis and intelligent control of uncertain impulsive stochastic nonlinear systems with applications

Abstract

A new operator is proposed for uncertain impulsive stochastic nonlinear systems (UISNSs) based on the T-S fuzzy model and the pole configuration principle. The definition of interval stability of the system is given using this operator. The application of interval stability theory to parameter uncertain systems is extended. Different from the general concept of stability, interval stability can not only determine the stability of the system but also reflect the convergence rate (CR) of the system. The fuzzy state feedback controllers with adjustable CR are further designed. Compared with most existing fuzzy controllers, our designed controllers can control the system more accurately, i.e., effectively constrain the CR of the system. Moreover, a new design method for an $H_{\infty }$ fuzzy controller based on interval stability is proposed, which can constrain the CR of the system while satisfying certain performance. Finally, the feasibility and applicability of these methods are verified by Chua's circuit model, the cart inverted pendulum model, and numerical experiments.