LMI Optimization Approach to Robust H∞ Filtering for Discrete-Time Nonlinear Uncertain Systems

A new approach for the design of robust H∞ filter for a class of discrete-time Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities. Thanks to the linearity of the proposed LMIs in both the admissible Lipschitz constant of the system and the disturbance attenuation level, they can be simultaneously optimized through convex optimization. The resulting H∞ observer guarantees exponential stability of the estimation error dynamics with guaranteed decay rate and is robust against time-varying parametric uncertainties. The proposed observer has also an extra important feature, robustness against nonlinear additive uncertainty. Explicit norm-wise and elementwise bounds on the tolerable nonlinear uncertainty are derived.