Robust ℋ∞ observer-based controller for lipschitz nonlinear discrete-time systems with parameter uncertainties

This note focuses on the design of an observer-based controller for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties. Thanks to the reformulated Lipschitz property [1] that take into account all the properties of the nonlinearities of the system combined with some mathematical tools, it is shown that the solution of the discrete-time output feedback problem, expressed in term of Linear Matrix Inequality (LMI), is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. This latter leads to a less restrictive synthesis condition than those available in the literature. A numerical example is provided in order to show the validity and superiority of the proposed method.