Stability Analysis for Continuous-Time Positive Systems With Time-Varying Delays

被引：251
作者：
Liu, Xingwen [1 ,2 ]
Yu, Wensheng [3 ]
Wang, Long [4 ,5 ]
机构：
[1] SW Univ Nationalities China, Coll Elect & Informat Engn, Chengdu 610041, Sichuan, Peoples R China
[2] Univ Elect Sci & Technol China, Sch Automat Engn, Chengdu 610054, Sichuan, Peoples R China
[3] E China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China
[4] Peking Univ, Coll Engn, Ctr Syst & Control, Beijing 100871, Peoples R China
[5] Peking Univ, Minist Educ, Key Lab Machine Percept, Beijing 100871, Peoples R China
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2010年 / 55卷 / 04期
基金：
美国国家科学基金会;
关键词：
Asymptotic stability; linear copositive Lyapunov functional; positive system; time-varying delays; NONNEGATIVE REALIZATION; LINEAR-SYSTEMS; STABILIZATION;
D O I：
10.1109/TAC.2010.2041982
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 note addresses the stability problem of continuous-time positive systems with time-varying delays. It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix. The result is a time-varying version of the widely-known asymptotic stability criterion for constant-delay positive systems. A numerical example illustrates the correctness of our result.
引用
收藏
页码：1024 / 1028
页数：5
相关论文
共 35 条
[1]   Nonnegative realization of a linear system with nonnegative impulse response [J].
Anderson, BDO ;
Deistler, M ;
Farina, L ;
Benvenuti, L .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1996, 43 (02) :134-142
[2]  
[Anonymous], 2000, PUR AP M-WI
[3]   Positive and compartmental systems [J].
Benvenuti, L ;
Farina, L .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (02) :370-373
[4]  
Benvenuti L., 2003, LECT NOTES CONTROL I
[5]  
Berman A., 1989, Nonnegative matrices in dynamic systems, V3
[6]  
Buslowicz M, 2007, B POL ACAD SCI-TECH, V55, P1, DOI 10.4064/ba55-1-1
[7]   On the Stability of Positive Linear Switched Systems Under Arbitrary Switching Laws [J].
Fainshil, Lior ;
Margaliot, Michael ;
Chigansky, Pavel .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (04) :897-899
[8]   An improved stabilization method for linear time-delay systems [J].
Fridman, E ;
Shaked, U .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (11) :1931-1937
[9]   Control for stability and positivity: Equivalent conditions and computation [J].
Gao, HJ ;
Lam, J ;
Wang, CH ;
Xu, SY .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2005, 52 (09) :540-544
[10]   Stability theory for nonnegative and compartmental dynamical systems with time delay [J].
Haddad, WM ;
Chellaboina, VS .
SYSTEMS & CONTROL LETTERS, 2004, 51 (05) :355-361
1234