On finite time and practical stability of linear discrete time delay systems

In the first part of this article, an overview of the results in non-Lyapunov stability was presented. Non-Lyapunov stability incorporates different types of stability such as: finite time stability, technical stability, practical stability, final stability etc. The article deals with a class of linear discrete time delay systems. The new approach in investigation of the particular class of control systems resulted in establishing new sufficient conditions of practical and finite time stability for discrete time delay systems. Consequently, the attractive practical stability has been introduced. The stability conditions are independent of time delay. Furthermore, to solve many convex optimization problems for the specific class of the discrete systems, it is not necessary to solve complex linear matrix inequalities. The conditions for practical instability have been introduced as well.