Lyapunov and Non-Lyapunov Stabilty of Linear Discrete Time Delay Systems

This paper extends some of the basic results in the area of Lyapunov (asymptotic) and finite time and practical stability to linear, discrete, time invariant time-delay systems. New definitions have been established for the latter concept of stability. Sufficient conditions for this type of stability, concerning the particular class of linear discrete time-delay systems are derived. More over the generalization of some previous results, in the area of Lyapunov stability for the same class of systems has been also established and proved.