Observer design for one-sided Lipschitz discrete-time systems

This note focuses on state observer design for a general class of nonlinear discrete-time systems that satisfies the one-sided Lipschitz condition. It has been shown that this condition may encompass a large class of nonlinearities. However, challenging problems arise such as relevant choice of the Lyapunov function or non convexity of the obtained stability conditions. Both full-order and reduced-order observer designs are considered. In this work, the main contribution is to provide first some mathematical artifacts on the Lyapunov function to obtain simple and workable stability conditions, furthermore we show how to obtain LMI conditions to ensure asymptotic convergence. On the other hand, we extend the obtained results to n − p reduced order observer design. High performances are shown through simulation results.