Robust static output feedback stabilization of discrete-time nonlinear uncertain systems with H∞ performance

A new approach for the design of robust static output feedback controller for a class of discrete-time Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities. The controller has also a guaranteed disturbance attenuation level (H
_infin
performance). 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 multiobjective optimization. The optimization over Lipschitz constant adds an extra important and new feature to the controller, robustness against nonlinear uncertainty. The resulting controller is robust against both nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit norm-wise and element-wise bounds on the tolerable nonlinear uncertainty are derived.