A result on common quadratic Lyapunov functions

被引：138
作者：
Shorten, R [1 ]
Narendra, KS
Mason, O
机构：
[1] NUI, Hamilton Inst, Maynooth, Kildare, Ireland
[2] Yale Univ, Ctr Syst Sci, New Haven, CT 06520 USA
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2003年 / 48卷 / 01期
关键词：
quadratic stability; stability theory; switched linear systems;
D O I：
10.1109/TAC.2002.806661
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this note, we define strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the nonexistence of a strong CQLF, for a pair of LTI systems, is characterized by easily verifiable algebraic conditions. These conditions are found to play an important role in proving the existence of strong CQLFs for general LTI systems.
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页码：110 / 113
页数：4
相关论文
共 10 条
[1]   Set of matrices with common Lyapunov solution [J].
Ando, T .
ARCHIV DER MATHEMATIK, 2001, 77 (01) :76-84
[2]   A NECESSARY AND SUFFICIENT CRITERION FOR THE STABILITY OF A CONVEX SET OF MATRICES [J].
COHEN, N ;
LEWKOWICZ, I .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1993, 38 (04) :611-614
[3]  
HERSHKOWITZ D, SIAM J MATRIX ANAL A, V715
[4]   Basic problems in stability and design of switched systems [J].
Liberzon, D ;
Morse, AS .
IEEE CONTROL SYSTEMS MAGAZINE, 1999, 19 (05) :59-70
[5]   RANGES OF REAL LYAPUNOV TRANSFORMATIONS [J].
LOEWY, R .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 13 (1-2) :79-89
[6]  
MASON O, 2002, SS200205 NUI
[7]   CRITERIA OF ASYMPTOTIC STABILITY OF DIFFERENTIAL AND DIFFERENCE INCLUSIONS ENCOUNTERED IN CONTROL-THEORY [J].
MOLCHANOV, AP ;
PYATNITSKIY, YS .
SYSTEMS & CONTROL LETTERS, 1989, 13 (01) :59-64
[8]  
Mori Y, 1998, IEEE DECIS CONTR P, P2808, DOI 10.1109/CDC.1998.757882
[9]  
Shorten R. N., 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), P1410, DOI 10.1109/ACC.1999.783600
[10]   Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems [J].
Shorten, RN ;
Narendra, KS .
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, 2002, 16 (10) :709-728
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