Stability test of multidimensional discrete-time systems via sum-of-squares decomposition

被引：18
|
作者：
Dumitrescu, B [1 ]
机构：
[1] Tampere Univ Technol, TICSP, FIN-33101 Tampere, Finland
来源：
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS | 2006年 / 53卷 / 04期
基金：
芬兰科学院;
关键词：
multidimensional systems; stability; positive polynomials; sum-of-squares; semidefinite programming;
D O I：
10.1109/TCSI.2005.859624
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
A new stability test for d-dimensional discrete-time systems is presented. It consists of maximizing the minimum eigen-value of a positive definite Gram matrix associated with a polynomial positive on the unit d-circle. This formulation is based on expressing the polynomial as a sum-of-squares and leads to a semidefinite programming (SDP) problem. Several heuristics are introduced for reducing the complexity of the problem in the case of sparse polynomials. Although in its practical form the test is based on a sufficient condition, the experimental results show that correct stability decisions are given. Comparisons with previous methods are favorable.
引用
收藏
页码：928 / 936
页数：9
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