Feedback control of a class of nonlinear discrete systems with state time-varying delay

In this paper, the robust stability under the feedback control of a class of nonlinear discrete systems with state time-varying delay is studied. Firstly, the robust stability´s sufficient condition of this system is given in the form of Linear Matrix Inequalities. Secondly, a state feedback controller of the system is designed, and the design method is a linear matrix inequality constrained optimization problem. In addition, the designed state feedback controller can make the closed loop system asymptotically stable. Finally, a numerical example and a simulation are given to illustrate the method´s feasibility and effectiveness.