Novel conditions for finite time stability of discrete time delay systems

In this article novel sufficient conditions for the practical and finite time stability of linear continuous system with time delay have been presented. A general mathematical description of the systems investigated was given as x(k+1)=A0x(k) + A1x(k-h). The proposed approach was based on the investigation of the Lyapunov-like functions which was used for derivation of the novel stability conditions, independent of time delay. The obtained results were applied to the investigation of systems' stability. The basic advantages of the presented conditions were the following: the functions used here did not have to be positive on the state space and there was no need for negative derivatives along the trajectory of systems.