Composite anti-disturbance resilient control for Markovian jump nonlinear systems with general uncertain transition rate

Abstract

In this paper, the issue of disturbance observer based resilient control is addressed for Markovian jump nonlinear systems with multiple disturbances and general uncertain transition rates. The disturbances are divided into two parts: one has a bounded $H_2$ norm, and the other is given by an exogenous system. The general uncertain transition rate matrix is composed of unknown elements and uncertain ones. The uncertain transition rate only has a known approximate range. First, the disturbance described by the exogenous system is estimated by a disturbance observer, and its estimation is used for the controller as feedforward compensation. Subsequently, by using the resilient control method, a composite anti-disturbance resilient controller is constructed to guarantee stochastic stability with $L_2-L_\infty$ performance of the closed-loop systems. Subsequently, the Lyapunov stability method and linear matrix inequality technique are applied to obtain the controller gain. Finally, an application example is provided to illustrate the effectiveness of the proposed approach.