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Dynamical robust ${H}_{\infty }$ filtering for nonlinear uncertain systems: an LMI approach. (English) Zbl 1202.93157
Summary: A new approach to robust ${H}_{\infty }$ filtering for a class of nonlinear systems with time-varying uncertainties is proposed in the LMI framework based on a general dynamical observer structure. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions and appear in both state and measured output equations. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting ${H}_{\infty }$ observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty.
##### MSC:
 93E11 Filtering in stochastic control 93C10 Nonlinear control systems 93B36 ${H}^{\infty }$-control 93D20 Asymptotic stability of control systems