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The Stability Analysis of Two Kinds of Systems

Author: FangQingXia
Tutor: LiuJianZhou
School: Xiangtan University
Course: Operational Research and Cybernetics
Keywords: Grey discrete systems Asymptotically stable Lyapunov function Singular large scale systems
CLC: TP13
Type: Master's thesis
Year: 2008
Downloads: 30
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Abstract


Stability is disturbed role , its movement to return to the original equilibrium a performance , it is a basic feature of the automatic control system should meet the stability control system to normal operation premise . Stability characterization systems movement behavior of a class of important structural features in accordance with the different requirements of the system design , the stability of the system can be categorized as the the external description based on the input and output stability and internal stability based on state-space description . while for linear time-invariant normal system , internal stability is the asymptotic stability , but also the stability theory of most importance and universality of the problem . stability control system performance , the system can work properly . now to analyze stability of the following two types of control systems . the special matrix analysis methods and techniques , interval matrix mold largest matrix L elements of nature to explore the matrix L subscript set N = {1,2 , · ·, n} divided structure matrix L similar to the diagonal matrix , to discuss the stability of of gray linear discrete system . Secondly, through discussions matrix L with the masters of nature p matrix L [γ] nature , get a linear gray discrete system criterion , and use of the Lyapunov function method gives a sufficient condition for its corresponding nonlinear gray discrete system stability issues . Finally, a numerical example illustrates the validity of the results , improved and promotion of the recently concluded third chapter discusses the stability of the generalized system , it is a very important issue , exert control target is to make the system stable , an unstable system is of no use value all isolated subsystems are regular , pulse free and asymptotically stable conditions of Lyapunov function method and linear matrix inequalities combined to study the stability of the generalized linear systems and generalized nonlinear system , given them a stable new sufficient criteria are to avoid difficulties in seeking the solution of the Lyapunov equation , the lifting of the restrictions associated parameter domain , and can use the Matlab LMI Toolbox to solve numerical examples are given to illustrate the results of the effectiveness of .

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