Static Output Feedback Control for Nonlinear Systems subject to Parametric and Nonlinear Uncertainties
For control engineers, this offers a robust controller design method for nonlinear systems with both parametric and nonlinear uncertainties, though it is an incremental extension of existing LMI-based techniques.
This paper designs a static output feedback controller for discrete-time nonlinear systems with Lipschitz continuity and time-varying uncertainties, achieving guaranteed H∞ performance. The LMIs allow simultaneous optimization of the Lipschitz constant and disturbance attenuation level, providing explicit bounds on nonlinear uncertainty.
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.