Disturbance‐observer‐based‐control and L 2 − L ∞ resilient control for Markovian jump non‐linear systems with multiple disturbances and its application to single robot arm system

Abstract

In this study, the problem of disturbance-observer-based-control (DOBC) and L 2−L ∞ resilient control for Markovian jump non-linear systems with multiple disturbances is investigated. The disturbances are divided into two parts: one part is produced by an exogenous system and the other part is supposed to lie in the space of L 2[0,∞). A disturbance observer is designed to estimate the first one, and the disturbance estimation is introduced into L 2−L ∞ resilient state feedback control law. Hence, by combining DOBC and L 2−L ∞ control methods, a composite anti-disturbance controller is designed to attenuate and reject two kinds of disturbances. Some sufficient conditions are obtained by using Lyapunov function method and linear matrix inequalities technique. Finally, an application example is given to illustrate the effectiveness of the main algorithm.