Robust stability analysis of discrete-time linear systems with time delay

The sufficient conditions of stability for discrete-time linear systems with time delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. In this paper, the stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of discrete-time linear systems with time delay, the system being stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. An example shows the practicability of these methods.