Conditions on the stability of a class of second-order switched systems

被引：34

作者：

Akar, M ^{[1
]}

Paul, A

Safonov, MG

Mitra, U

机构：

[1] Natl Univ Ireland, Hamilton Inst, Maynooth, Kildare, Ireland

[2] Marger Johnson McCollom, Portland, OR 97204 USA

[3] Univ So Calif, Dept Elect Engn Syst, Los Angeles, CA 90089 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2006年 / 51卷 / 02期

基金：

美国国家科学基金会;

关键词：

common quadratic Lyapunov function (CQLF); M-matrix; stability; switched systems;

D O I：

10.1109/TAC.2005.863512

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For a special class of systems, it is shown that the existence of a common quadratic Lyapunov function (CQLF) is necessary and sufficient for the stability of an associated switched system under arbitrary switching. Furthermore, it is shown that the existence of a CQLF for N (N > 2) subsystems is equivalent to the existence of a CQLF for every pair of subsystems. An algorithm is proposed to compute a CQLF for the subsystems, when it exists, using the left and right eigenvectors of a critical matrix obtained from a matrix pencil.

引用

页码：338 / 340

页数：3

共 11 条

[1] On the existence of common quadratic Lyapunov functions for second-order linear time-invariant discrete-time systems [J].

Akar, M ;

Narendra, KS .

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, 2002, 16 (10) :729-751

[2]

Bapat RB., 1997, NONNEGATIVE MATRICES

[3]

Berman A., 1994, CLASSICS APPL MATH, DOI [10.1016/C2013-0-10361-3, 10.1137/1.9781611971262, DOI 10.1137/1.9781611971262]

[4] A converse Lyapunov theorem for a class of dynamical systems which undergo switching [J].

Dayawansa, WP ;

Martin, CF .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (04) :751-760

[5]

Fiedler M., 1962, CZECH MATH J, V12, P382, DOI [10.21136/CMJ.1962.100526, DOI 10.21136/CMJ.1962.100526]

[6] A SIMPLE DISTRIBUTED AUTONOMOUS POWER-CONTROL ALGORITHM AND ITS CONVERGENCE [J].

FOSCHINI, GJ ;

MILJANIC, Z .

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, 1993, 42 (04) :641-646

[7]

GURVITS L, 2004, P MTNS LEUV BELG JUL

[8]

Horn RA., 2013, Topics in Matrix Analysis, V2nd ed, DOI DOI 10.1017/CBO9780511840371

[9]

Liberzon D., 2003, SYS CON FDN

[10]

Paul A, 2004, P AMER CONTR CONF, P1655

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