DEVELOPMENT OF HOMOGENEITY CONCEPT FOR TIME-DELAY SYSTEMS

被引：34
作者：
Efimov, D. [1 ,2 ,3 ]
Perruquetti, W. [1 ,2 ]
Richard, J. -P. [1 ,2 ]
机构：
[1] Inria, Non A Team, F-59650 Villeneuve Dascq, France
[2] Ecole Cent Lille, LAGIS UMR CNRS 8219, F-59651 Villeneuve Dascq, France
[3] Univ ITMO, Dept Control Syst & Informat, St Petersburg 197101, Russia
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 03期
关键词：
time-delay systems; homogeneity; input-to-state stability; instability; NONLINEAR-SYSTEMS; DIFFERENTIAL EQUATIONS; ASYMPTOTIC STABILITY; OBSERVER DESIGN; VECTOR FIELD; STABILIZATION; STABILIZABILITY; APPROXIMATIONS; NILPOTENT; FEEDBACK;
D O I：
10.1137/130908750
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The notion of homogeneity is extended to time-delay nonlinear systems. Applications of Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions for stability investigation are analyzed. The notion of local homogeneity is introduced, relations between stability/instability of the locally approximating dynamics and the original time-delay system are established. A link between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.
引用
收藏
页码：1547 / 1566
页数：20
相关论文
共 37 条
[1]  
Aleksandrov AY, 2012, SIBERIAN MATH J+, V53, P393
[2]   Homogeneous approximation, recursive observer design, and output feedback [J].
Andrieu, Vincent ;
Praly, Laurent ;
Astolfi, Alessandro .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (04) :1814-1850
[3]  
[Anonymous], 1991, LECT NOTES PURE APPL
[4]  
[Anonymous], 2010, P IFAC NOLCOS S
[5]  
[Anonymous], 2001, LECT NOTES CONTROL I
[6]  
[Anonymous], P EUR CONTR C ECC 20
[7]  
Asl FM, 2000, P AMER CONTR CONF, P2496, DOI 10.1109/ACC.2000.878632
[8]   Verification of ISS, iISS and IOSS properties applying weighted homogeneity [J].
Bernuau, Emmanuel ;
Polyakov, Andrey ;
Efimov, Denis ;
Perruquetti, Wilfrid .
SYSTEMS & CONTROL LETTERS, 2013, 62 (12) :1159-1167
[9]   Geometric homogeneity with applications to finite-time stability [J].
Bhat, SP ;
Bernstein, DS .
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2005, 17 (02) :101-127
[10]   D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems [J].
Bokharaie, Vahid Samadi ;
Mason, Oliver ;
Verwoerd, Mark .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (12) :2882-2885
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