ON STATE FEEDBACK AND OBSERVERS FOR A CLASS OF DELAY DISCRETE-TIME NONLINEAR SYSTEMS

In this paper, we consider the problem of bounded state feedback stabilization and observers design of a class of nonlinear discrete-time delay systems. From an appropriate Lyapunov function and judicious mathematical manipulations, we deduce a simple LMI conditions (that may be checked easily) to ensure asymptotic stability of both the state feedback and the observer. First, we provide an explicit bounded state feedback law that may seen as generalization of the existing results in the nonlinear field. On the other hand, we present a useful and systematic approach to design observers for discrete-time systems with unknown delay. To illustrate performances of the proposed approach, a numerical example is provided.