Static Output Feedback Control for Nonlinear Systems subject to Parametric and Nonlinear Uncertainties

TL;DR

This paper presents a convex optimization-based method for designing static output feedback controllers that ensure stability and disturbance attenuation for nonlinear systems with parametric and nonlinear uncertainties.

Contribution

It introduces a novel LMI-based approach that simultaneously optimizes Lipschitz constant and disturbance attenuation, enhancing robustness against uncertainties.

Findings

Controller guarantees stability and performance under uncertainties.

Explicit bounds on tolerable nonlinear uncertainties are derived.

Method is applicable to discrete-time nonlinear systems with time-varying uncertainties.

Abstract

This work addresses the design of static output feedback control of discrete-time nonlinear systems satisfying a local Lipschitz continuity condition with time-varying uncertainties. The controller has also a guaranteed disturbance attenuation level (Hinfty 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.