Polynomial Multi-parameter Dependent System Stability Analysis

As one important class of systems with uncertainty, based on the form of parameter-dependent the parameter uncertain system can be divided into affine linear and polynomial-type This artical directed at single- parameter uncertain continuous-time system of the polynomial type, it takes full advantage of S-procedure approach and introduces of redundant variables (matrix) parameters of the skills to deal with the parameter constraints and to make conservative lower reflected by the examples,the Sufficient criteria of the robust stable was given by LMI.The reasult of the simulation showed that it is important to select the appropriate order parameters in the parameter-dependent Lyapunov function and redundant variable.The parameters of low order and no application redundancy variable will increase the results of the conservative while high-order parameters and too many redundant variables may not be able to improve the conservative, but a surge in the cost of computing.To the twice- parameter uncertain continuous-time system of the polynomial type,in the case of the same parameter boundary as the simplification assumed condition,use the same method to analysis the robust stable and exponent stable,abtained the stable criteria.This paper not only considers the robust stability, but also increases robust stability of the convergence rate;we also get the widest stable boundary of the parameter variation in the assumption of the system is stable.Because the usual non-linear function systems can be approximately representated by polynomial of appropriately order,the research of this paper have theoretical significance in the approving the study of non-linear systems.