A Generalized Robust Filtering Framework for Nonlinear Differential-Algebraic Systems

A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to be affected by norm-bounded disturbance and to have both norm-bounded uncertainties in the realization matrices as well as nonlinear model uncertainties. We synthesize a robust Hinfty filter through semidefinite programming and strict linear matrix inequalities (LMIs). The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting Hinfty filter 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. Explicit bound on the tolerable nonlinear uncertainty is derived based on a norm-wise robustness analysis.