Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions
- 作者：Ricardo C.L.F. Oliveira ; Maurí ; cio C. de Oliveira ; Pedro L.D. Peres
- 关键词：Robust stability ; Robust none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V4X-4S1JJX7-2&_mathId=mml31&_user=1067359&_cdi=5770&_rdoc=12&_acct=C000050221&_version=1&_userid=10&md5=923287d06c
- 刊名：Systems and Control Letters
- 出版年：2008
- 期刊代码：171_01676911
- 类别：et
- 出版时间：August 2008
- 卷：57
- 期：8
- 页码：680-689
- 文件大小：381 K
摘要
This paper investigates the problems of checking robust stability and evaluating robust 
2 performance of uncertain continuous-time linear systems with time-invariant parameters lying in polytopic domains. The novelty is the ability to check robust stability by constructing a particular parameter-dependent Lyapunov function which is a polynomial function of the uncertain system matrices, as opposed to a general polynomial function of the uncertain parameter. The degree of the polynomial is tied to a certain integer κ. The existence of such Lyapunov function can be proved by solving parameter-dependent Linear Matrix Inequalities (LMIs), which are guaranteed to be solvable for a sufficiently large yet finite value of κ whenever the system is robustly stable. Extensions to guaranteed 2 cost computation are also provided. Numerical aspects concerning the programming and the evaluations of the proposed tests are discussed and illustrated by examples.
2 performance of uncertain continuous-time linear systems with time-invariant parameters lying in polytopic domains. The novelty is the ability to check robust stability by constructing a particular parameter-dependent Lyapunov function which is a polynomial function of the uncertain system matrices, as opposed to a general polynomial function of the uncertain parameter. The degree of the polynomial is tied to a certain integer κ. The existence of such Lyapunov function can be proved by solving parameter-dependent Linear Matrix Inequalities (LMIs), which are guaranteed to be solvable for a sufficiently large yet finite value of κ whenever the system is robustly stable. Extensions to guaranteed 2 cost computation are also provided. Numerical aspects concerning the programming and the evaluations of the proposed tests are discussed and illustrated by examples.