A generalized framework for robust nonlinear H∞H∞ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties

In this paper, a generalized robust nonlinear H∞H∞ filtering method is proposed for a class of Lipschitz descriptor systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to have norm-bounded uncertainties in the realization matrices as well as nonlinear uncertainties. We synthesize the H∞H∞ filter through semidefinite programming and strict LMIs. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting H∞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.