The Study On Robust Stability For Discrete Systems

Discrete systems are a kind of control system existing extensively in thepractical problems , however,for there are the limitations of cognitive level ofa disturbance inside and outside . People get information which is uncertain.Therefore, the discussion of such imprecise discrete systems, in particular thestability issue is very significant.It has had an important role and significance inthe practice of matrix algebra, control theory, ecosystems, economic mathematics,engineering and many other fields. In recent years, many scholars in china andabroad have explored and studied a great deal of its character and determination,and they have achieved many important results.This article is mainly based on the system of state-space model, on thebasis of some recent literature using analytical methods and the matrix secondLyapunov method to study grey discrete systems and discrete uncertain systemsRobust stability, giving the determine ways of some direct determinations ofthe asymptotic stability. And this article improves and promotes a number ofconclusions. At the same time the main results are extended to the major findingsof a disturbance with nonlinear systems. Main contents as follows:Chapterâ… This paper introduces the dynamic system of state-space model,the concept of stability, the Grey discrete system and uncertainty discrete sys-tems, as well as discrete generalized system of background research and the statusquo of which is the main work.Chapterâ…¡Uses special matrix analysis method,by constructing positivediagonal matrices and applying some techniques of inequalities,we acquire severalnew practical su?cient conditions of the robust stability of gray discrete systemsseveral new practical su?cient conditions for the improvement and promotionof some of the findings of the recent literature, and its further discussions withnonlinear disturbance situation. And illustrates the e?ectiveness and superiorityby numerical examples.Chapterâ…¢Discusses discrete uncertain systems in several uncertainties as-sumptions (non-structural uncertainty, strong structural uncertainty, and morecell-matrix structure uncertainty, norm-bounded uncertainty), and gives the cor-responding system robust stability criterion and the corresponding numericalexamples. At the same time the conclusions will be further extended to the non-linear disturbances discrete uncertain systems.