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 Itô-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.

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Correspondence to Anhua Wan.

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Mao, W., Deng, F. & Wan, A. Robust H 2/H global linearization filter design for nonlinear stochastic time-varying delay systems. Sci. China Inf. Sci. 59, 32204 (2016). https://doi.org/10.1007/s11432-015-5386-7

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Keywords

  • global linearization method
  • mixed H 2/H filtering
  • nonlinear filtering
  • Hamilton-Jacobi inequality
  • Lyapunov–Krasovskii functional
  • nonlinear stochastic time-varying delay system