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 H∞ 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 H∞ 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. keywords : Robust Filtering, Nonlinear H∞, Differential Algebraic Equations, Descriptor Systems, Semidefinite Programming