Design of unknown input observer for discrete-time Markov jump systems with unknown input in both state equation and output equation

Abstract

The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is studied. First, like a normal system, the whole nonlinear system is transformed into a local linear system, and then a large number of linear system theories can be applied to solve related problems. Second, in the observer design of general discrete-time Markov jump systems, only the unknown input in the state equation is usually considered. In this paper, the unknown input is considered in both the state equation and the output equation. The state estimation error system is derived by defining the error. The non-uniform Lyapunov functional is selected to stabilize the estimation error system using the Lyapunov theory. The sufficient conditions for the stability of the system are obtained and transformed into the feasibility problem of linear matrix inequality. The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is solved using MATLAB software. Finally, a numerical example of two rules and two modes is used to verify the effectiveness and feasibility of the proposed unknown input observer.