Construction of iISS Lyapunov functions for interconnected parabolic systems

被引：0

作者：

Mironchenko, Andrii ^{[1
,2
]}

Ito, Hiroshi ^{[1
]}

机构：

[1] Kyushu Inst Technol, Dept Syst Design & Informat, 680-4 Kawazu, Iizuka, Fukuoka 8208502, Japan

[2] Univ Passau, D-94032 Passau, Germany

来源：

2015 EUROPEAN CONTROL CONFERENCE (ECC) | 2015年

关键词：

SMALL-GAIN THEOREM; STATE STABILITY; INPUT;

D O I：

暂无

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 paper develops tools to construct Lyapunov functions establishing integral input-to-state stability (iISS) and input-to-state stability (ISS) for several classes of nonlinear parabolic equations. Using these constructions and an infinite-dimensional iISS small-gain theorem we provide a stability criterion for interconnections of iISS parabolic systems. We show that for interconnections of partial differential equations it is essential to choose right state and input spaces, especially for iISS subsystems which are not ISS.

引用

下载

页码：37 / 42

页数：6

共 50 条

[41] On the construction of the Lyapunov functions
Propoi, AI
DOKLADY AKADEMII NAUK, 2000, 371 (06) : 739 - 741
[42] ON CONSTRUCTION OF LYAPUNOV FUNCTIONS
BURTON, TA
SIAM JOURNAL ON APPLIED MATHEMATICS, 1969, 17 (06) : 1078 - &
[43] Spatial Decay Analysis in Interconnected Dynamical Systems Using Vector Lyapunov Functions
Deroo, Frederik
Hirche, Sandra
Anderson, D. O.
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 3654 - 3660
[44] Small-gain conditions and Lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption
Ito, Hiroshi
Jiang, Zhong-Ping
2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12, 2008, : 2297 - +
[45] COMPUTER GENERATED LYAPUNOV FUNCTIONS FOR INTERCONNECTED SYSTEMS - IMPROVED RESULTS WITH APPLICATIONS TO POWER-SYSTEMS
MICHEL, AN
NAM, BH
VITTAL, V
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1984, 31 (02): : 189 - 198
[46] A Lyapunov-Krasovskii methodology for iISS of time-delay systems
Pepe, P.
Jiang, Z. -P.
PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 4208 - +
[47] Compositional Construction of Control Barrier Functions for Interconnected Control Systems
Jagtap, Pushpak
Swikir, Abdalla
Zamani, Majid
PROCEEDINGS OF THE 23RD INTERNATIONAL CONFERENCE ON HYBRID SYSTEMS: COMPUTATION AND CONTROL (HSCC2020) (PART OF CPS-IOT WEEK), 2020,
[48] Stability criteria for interconnected iISS systems and ISS systems using scaling of supply rates
Ito, H
PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, : 1055 - 1060
[49] Establishing iISS property of interconnected systems via parametrization of supply rates
Ito, Hiroshi
2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE, VOLS 1-8, 2005, : 5650 - 5655
[50] Construction of Lyapunov Functions for Homogeneous Second-Order Systems
Lopez-Ramirez, Francisco
Sanchez, Tonameti
Moreno, Jaime A.
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 5494 - 5499

← 1 2 3 4 5 →