The Stability Analysis Of Two Kinds Of Systems

The stability refers to a capability of the system after receiving the perturba-tion function, its movement may return to the original state of equilibrium. Thestability is a basic characteristic which all automatic control system should satisfy.Stable is the premise of normal operation of the control systems. The stabilityis a kind of important structural feature of the representative system movementbehavior . According to system design's various requirement, the system stabil-ity may classify to exterior stability based on the input output description andinternal stability based on the state space description .For normal linear time-invariant systems, internal stability equals to asymptotic stability, and it's thestability theory's most important and universal research problem in stability the-ory. The stability is an important capability of control system,and it is also themain condition for the normal operation of the system. Now let's analyze thestability of the following two kinds of control systems .The second chapter applies the special matrix theory's methods and skills,through investigation the properties of the maximal matrix L's elements of in-terval matrix's model matrix, the index set of the matrix L N = {1,2,···,n} isdivided to construct diagonal similarity matrix of the matrix L.We discuss thestability of liner gray discrete system.Secondly, we get some criterion of liner graydiscrete system through the discussion of the properties of principal submatrixmatrix L[γ] possessing p in matrix L,and achieves some new su?cient conditionsfor identifying the stability of non-liner gray discrete systems through Lyapunovfunction. Finally, We give some examples to illustrate the e?ectiveness of theresults in order to improve and promote the recent results.The third chapter discusses the stability of large-scale system, Which is avery important problem. The first objective of Exerting control is to stabilizesystem, since it is no value to study a unstable system. In this paper,we ana-lyze the asymptotic stability of singular linear and non-linear large-scale systemby the means of Lyapunov function and LMI under the condition that all iso-lated subsystems are regularity,impulse immunity and stability ,and achieve newsu?cient conditions for identification.This method avoids the di?culties in thesolving the Lyapunov equation, relieves the limitation of the domain of the as-sociated parameters, and can be solved by Matlab LMI toolbox. Finally,we give some examples to illustrate the e?ectiveness of the results.