Abstract
The stability analysis and controller design of discrete linear systems with time-varying delay are addressed. Firstly, the uniformly asymptotical stability criterion with adjustable parameter is derived by Lyapunov-Razumikhin approach. Then, the stabilization approaches for linear systems with time delay by state feedback and observer based-on state feedback are also presented. Sufficient conditions for the existence of state feedback gain and the observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities. Compared with methods in the references, the dynamic performance of systems, such as the overshoot and the convergence rate of the response, can be adjusted by changing the adjustable parameter. Lastly, an illustrative example is given to show the effectiveness of the proposed.
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