Approach To The Relative Stability Of Large-scale Generalized System And Grey Discrete System

In the design of the control system, the stability of the system is one of the most important problems which are concerned by people. No matter for normal linear systems, Large-scale linear descriptor systems or for uncertain grey discrete dynamic systems, unstable systems always worth nothing practically. Especially because of the particularity and complexity of large-scale generalized systems and grey discrete dynamic systems, researches on the stability of these systems possess a large practical and theoretical significance. This thesis mainly uses Lyapunov function method combined with control inequation method and academic knowledge of matrix to put forward some adequate conditions for the stability and equanimity of large-scale interconnected systems and grey discrete dynamic systems on the basis of existed achievements. The contributions of this thesis are as follows:Firstly the writer uses control inequation method and academic knowledge of matrix and puts forward a matrix of concentrated parameters through the studies on the positive definiteness of the block matrix and the concentrated parameter method, and applies this matrix of concentrated parameters to the decentralization and equanimity of the large-scale generalized systems. This method can not only advance the results of the existed concentrated parameters, but also broaden the applied scope of the systems. This thesis explains and validates the main results through examples of numerical value.Secondly this thesis studies on the asymptoctic stability and equanimity of a kind of large-scale interconnected systems under the premiss with or without impulse, puts forward a problem of the asymptoctic stability of a kind of large-scale interconnected systems through an analytic method which brings in a Lyapunov function and a peculiar matrix, then presents a method for the equanimity of the systems by proposing a new Riccati equation. At last, this thesis validates the theorems through the numerical value emulation experiment.Lastly this thesis does some researches on the stability of a kind of grey discrete dynamic systems, brings in diagonal similarity character and techniques of inequalities on the basis of existed achievements, puts forward some methods for the judgement of discrete stability to improve the existed conclusions, finally this thesis validates the feasibility of the conclusion through the numerical value emulation experiment.