Stability Analysis Of Linear Time-delay Difference Systems

Stability is the premise for the normal operation of the actual systems.In order to apply the computers as the auxiliary tool to analyze and control the system,the discretization of continuous-tme systems is required by researchers.The time delay is an ubiquitous phenomenon in nature,and it often impacts the stability of the systems.The linear delay difference systems are very important in the compute simulations of the continuous-time systems.Therefore,investigating the methods to analyze the stability of linear delay difference systems is very significant and valuable,and hence it has received extensive attention.This paper is concerned with the exponential stability analysis of linear delay difference systems.By constructing Lyapunov-Krasovskii functionals and applying the linear matrix inequality(LMI)method combined with summation inequalities based on weighted discrete orthogonal polynomials(WDOPs),we obtain sufficient conditions for the exponential stability and the decay rate estimation of explicit solutions of linear delay difference systems.The main contents of this thesis are described as follows:First,a set of WDOPs is established by using the so-called Gram-Schmidt or-thogonalization process,and then two WDOPs-based summation inequalities which including three parameters ?,m and vm are derived.If we take different and appro-priate values for these parameters,then these WDOPs-based summation inequalities turns into some existing ones,including the discrete Jensen inequality,the discrete Writinger inequalities,etc.Second,for the linear single delay difference systems,by designing an Lyapunov-Krasovskii functional,these WDOPs-based summation inequalities are applied to prove sufficient conditions for the exponential stability and the decay rate estimation of explicit solutions.The simulation results of two numerical examples indicate that our approach can arrive the larger decay rates than ones in references.Third,as an application of these WDOPs-based summation inequalities,we will give sufficient conditions for the exponential stability and the decay rate estimation of explicit solutions of linear double delay difference systems.Then the efficiency of the obtained theoretical results are illustrated by a numerical example.