Abstract
This paper deals with the problems of $H_{\infty }$ finite-time boundedness and finite-time $H_{\infty }$ state feedback stabilization for the discrete-time systems with time-varying delay and norm-bounded disturbance. We establish sufficient conditions to ensure a class of nonlinear discrete-time system with norm bounded disturbance is $H_{\infty }$ finite-time bounded. Then the result is extended to $H_{\infty }$ finite-time stabilization for a class of discrete-time systems with time-varying delay and norm-bounded disturbance. The state feedback controller is designed for $H_{\infty }$ finite-time stabilization. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.
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