Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems

Abstract

One can design a robust H ∞ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. In this paper, the robust mixed H 2/H ∞ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic Ito-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H ∞ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level, the H 2 globally linearized filtering problem with the worst case disturbance in the H ∞ filter case is known as the mixed H 2/H ∞ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation example is provided to illustrate the effectiveness of the proposed method.