Robust $H_{2} /H_{\infty}$ Global Linearization Filter Design for Nonlinear Stochastic Systems

This paper proposes a robust global linearization filter design for a nonlinear stochastic system with exogenous disturbance. The nonlinear dynamic system is modeled by Itocirc-type stochastic differential equations. For a general nonlinear stochastic system with exogenous disturbance, the robust
H

_infin
filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality (HJI). In general, it is difficult to solve the second-order nonlinear HJI. In this paper, based on the global linearization scheme, the robust
H

_infin
global linearization filter design for nonlinear stochastic systems is proposed via solving linear matrix inequalities (LMIs) instead of a second-order HJI. When the worst case disturbance attenuation of
H

_infin
filtering is considered, a suboptimal
H

₂
global linearization filtering problem is also solved by minimizing the upper bound on the
H

₂
norm of the estimation error variance. The suboptimal global linearization filtering design problem under a desired worst case disturbance attenuation (i.e., the mixed
H

₂
/
H

_infin
filtering design problem) is also transformed into a constrained optimization problem characterized in terms of LMI constraints, which can efficiently be solved by convex optimization techniques via the LMI toolbox of Matlab. Therefore, the proposed robust global linearization filter is potential for practical state estimation of nonlinear stochastic systems with intrinsic random fluctuation and external disturbance. A simulation example is provided to illustrate the design procedure and to confirm the expected robust filtering performance.