On non-Lyapunov stability of linear discrete time delay systems: LMIs approach

Abstract

This paper gives new contributions to the area of non-Lyapunov (finite time stability, technical stability, practical stability, final stability) for the particular class of linear discrete time delay systems. The idea of attractive practical stability is introduced for the first time. Moreover, based on the matrix inequalities and Lyapunov-like functions, some new sufficient conditions under which the linear discrete time delay system is finite time stable are given. Finally, an example is employed to verify the efficiency of the proposed Theorems as well as to show that results derived upon LMIs are less restrictive than those based on a classical approach. To the best knowledge of authors, such results have not been reported yet.