Observer-based Finite Time Dissipative Control for Nonlinear Discrete Time-varying System with Time-varying Delay

This paper addresses an observer-based finite time dissipative control problem for nonlinear discrete time-varying systems with time-varying delay. The nonlinear perturbation is subject to the Lipchitz condition. On the basis of a newly augment time-varying Lyapunov-like functional, delay-dependent conditions are obtained using the discrete Wirtinger-type inequality. The conditions ensure that the closed-loop system is finite time bounded (FTB) as well as the dissipative performance is satisfied. Then the observer-based time-varying control problem is achieved by solving a class of recursive linear matrix inequalities (RLMIs). Two examples illustrate the feasibility and superiority of the proposed method.