Lyapunov and non-Lyapunov stability of linear discrete time delay systems

Abstract

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. To the best knowledge of the authors, such results have not yet been reported. Moreover, the generalization of some previous results, in the area of Lyapunov stability for the same class of systems has been also established and proven.