Discrete time delayed system stability theory in the sense of Lyapunov: new results

Our aim is to improve the existing results concerning asymptotic stability of a particular class of linear discrete time delay systems. This work extends one of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. This result is given in the form of only sufficient conditions and represent further improvement of the existing results concerning the asymptotic stability of systems described by vector state representation of the form x(k +1) = A₀x(k) + A₁x(k-1). This result is less conservative than those in existing literature. To the best knowledge of the authors, such results have not yet been reported.