Construction of ISS Lyapunov functions for infinite networks of ISS systems

被引：0
|
作者：
Kawan, Christoph [1 ]
Mironchenko, Andrii [2 ]
Zamani, Majid [1 ,3 ]
机构：
[1] Ludwig Maximilians Univ Munchen, Inst Informat, D-80538 Munich, Germany
[2] Univ Passau, Fac Comp Sci & Math, D-94032 Passau, Germany
[3] Univ Colorado, Comp Sci Dept, Boulder, CO 80309 USA
来源：
2021 60TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC) | 2021年
基金：
欧盟地平线“2020”;
关键词：
large-scale systems; small-gain theorems; input-to-state stability; nonlinear systems; infinite-dimensional systems; SMALL-GAIN THEOREM; DISTRIBUTED CONTROL; STATE STABILITY; INPUT;
D O I：
10.1109/CDC45484.2021.9683184
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We show that an infinite network of input-to-state stable (ISS) systems, admitting ISS Lyapunov functions, itself admits an ISS Lyapunov function, provided that the couplings of the subsystems are sufficiently weak. The strength of the couplings is described in terms of the properties of the so-called gain operator, built from the interconnection gains. If the discrete-time system induced by a slightly scaled gain operator is uniformly globally asymptotically stable, an ISS Lyapunov function for the infinite network can be constructed.
引用
收藏
页码：4811 / 4816
页数：6
相关论文
共 50 条
  • [41] On Implicit Finite-Time and Fixed-Time ISS Lyapunov Functions
    Lopez-Ramirez, F.
    Efimov, D.
    Polyakov, A.
    Perruquetti, W.
    [J]. 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2018, : 706 - 710
  • [42] COMPUTATION OF LOCAL ISS LYAPUNOV FUNCTIONS WITH LOW GAINS VIA LINEAR PROGRAMMING
    Li, Huijuan
    Baier, Robert
    Gruene, Lars
    Hafstein, Sigurdur F.
    Wirth, Fabian R.
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (08): : 2477 - 2495
  • [43] A lyapunov function for interconnected ISS systems derived from dissipation inequalities
    Ito, Hiroshi
    Jiang, Zhong-Ping
    [J]. PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2007, : 1168 - 1173
  • [44] ISS Lyapunov functions for time-varying hyperbolic partial differential equations
    Prieur, Christophe
    Mazenc, Frederic
    [J]. 2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC), 2011, : 4915 - 4920
  • [45] Small-gain conditions and Lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption
    Ito, Hiroshi
    Jiang, Zhong-Ping
    [J]. 2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12, 2008, : 2297 - +
  • [46] Synchronous Interval Observer Design for Switched LPV Systems using Multiple Quadratic ISS-Lyapunov Functions
    Ifqir, S.
    Ait-Oufroukh, N.
    Ichalal, D.
    Mammar, S.
    [J]. 2017 25TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION (MED), 2017, : 388 - 393
  • [47] Converse Lyapunov-Krasovskii theorem for ISS of neutral systems in Sobolev spaces
    Efimov, Denis
    Fridman, Emilia
    [J]. AUTOMATICA, 2020, 118
  • [48] A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems
    Pepe, P.
    Jiang, Z. -P.
    [J]. SYSTEMS & CONTROL LETTERS, 2006, 55 (12) : 1006 - 1014
  • [49] A Lyapunov-Krasovskii methodology. for ISS of time-delay systems
    Pepe, P.
    Jiang, Z. -P.
    [J]. 2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE, VOLS 1-8, 2005, : 5782 - 5787
  • [50] ISS characterization of retarded switching systems with relaxed Lyapunov-Krasovskii functionals
    Haidar, Ihab
    Pepe, Pierdomenico
    [J]. 2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC), 2022, : 6242 - 6247
12345