Homogeneous Lyapunov functions for polynomial systems: a Tensor product approach

被引：0

作者：

Hajer, Bouzaouache ^{[1
]}

Naceur, Benhadj Braiek ^{[2
]}

机构：

[1] ISETCOM, Inst Super Etud Technol Commun, Ariana, Tunisia

[2] Ecole Polytech Tunis, LECCP, La Marsa, Tunisia

来源：

2007 IEEE INTERNATIONAL CONFERENCE ON CONTROL AND AUTOMATION, VOLS 1-7 | 2007年

关键词：

polynomial systems; Kronecker product; stability; homogeneous Lyapunov function; LMIs;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper shows that the Kronecker product and the properties of tensoriel algebra are useful tools for nun quadratic stability analysis. When using them, sufficient conditions for global asymptotic stability of polynomial systems can be easily derived in terms of LMI feasibility tests for the existence of homogeneous Lyapunov functions of even degree.

引用

页码：7 / +

页数：2

共 12 条

[1]

[Anonymous], SIAM

[2]

BLIMAN PA, 2000, 4014 INRIA

[3]

BOUZAOUACHE H, 2003, SAMS, V43

[4]

Braiek E. B., 1995, Systems Analysis Modelling Simulation, V17, P211

[5]

BRAIEK EB, 1996, SAMS J, V11, P11

[6] KRONECKER PRODUCTS AND MATRIX CALCULUS IN SYSTEM THEORY [J].

BREWER, JW .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1978, 25 (09) :772-781

[7]

CHESI G, 232002 DII

[8] A numerical method for the stability analysis of quasi-polynomial vector fields [J].

Gléria, IM ;

Figueiredo, A ;

Rocha, TM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (01) :329-342

[9] Computation of Lyapunov functions for smooth nonlinear systems using convex optimization [J].

Johansen, TA .

AUTOMATICA, 2000, 36 (11) :1617-1626

[10] A COMMON LYAPUNOV FUNCTION FOR STABLE LTI SYSTEMS WITH COMMUTING A-MATRICES [J].

NARENDRA, KS ;

BALAKRISHNAN, J .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1994, 39 (12) :2469-2471

← 1 2 →