Discrete time delayed system stability theory in the sense of Lyapunov: an application to chemical engineering and process technology

Abstract

Our aim is to improve the existing results concerning asymptotic stability of a particular class of linear discrete time delay systems. This paper 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. It has been shown the direct application, of results derived to the particular class of chemical processes. To the best knowledge of the authors, such result have not yet been reported.