Designing a Stochastic Adaptive Impulsive Observer for Stochastic Linear and Nonlinear Impulsive Systems

Abstract

State observation (estimation) is a very important issue in system analysis and control. This paper develops a new observer called Stochastic Adaptive Impulsive Observer (SAIO) for the state estimation of impulsive systems. The proposed observer is applicable to linear and nonlinear stochastic impulsive systems. In addition, the effect of parametric uncertainty is considered and unknown parameters of the system are estimated by suitable adaptation laws. Impulsive system theory, particularly stochastic Lyapunov‐like function, is used to analyze the stability and convergence of the state estimations. The main advantages of the proposed observer are: 1) it gives continuous estimation from discrete time measurements of the system output, and 2) it is useful for state estimation when continuous measurements are impossible or expensive. Simulation results show the effectiveness of the proposed observer and we believe that it has many applications in control and estimation theories.