  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.
