H_∞State Estimation for Linear Impulsive Systems with Stochastic Uncertainties

Abstract

In this paper we study the H_∞ state estimation problems for a class of linear continuous-time systems with impulsive effects, stochastic uncertainties and discrete-time observation on the finite time interval. The systems include linear stochastic discrete-time systems. We adopt game theoretic and variational approach, and derive the impulsive Riccati equation which gives the necessary condition for the solvability of the H_∞ estimation problems, the estimates and the form of H_∞ estimators by calculating the stochastic first variation of the performance index under the dynamics constraint. By this approach the H_∞ estimation problems are equivalent to the noncausal H_∞ tracking control problems for the stochastic impulsive systems.