Exponential Stability of Continuous-Time Piecewise Affine Systems

被引：0

作者：

Cabral, L. ^{[1
]}

Valmorbida, G. ^{[2
]}

da Silva Jr, J. M. Gomes ^{[3
]}

机构：

[1] Univ Fed Rio Grande, Programa Posgrad Engn Elect, BR-90035190 Porto Alegre, Brazil

[2] Univ Paris Saclay, Inria Project DISCO, CNRS, Cent Supelec, F-91190 Gif Sur Yvette, France

[3] Univ Fed Rio Grande, Dept Automat & Energy Syst, BR-90035190 Porto Alegre, Brazil

来源：

IEEE CONTROL SYSTEMS LETTERS | 2024年 / 8卷

关键词：

Vectors; Numerical stability; Germanium; Circuit stability; Trajectory; Stability criteria; System dynamics; Piecewise affine systems; stability analysis; semidefinite programming;

D O I：

10.1109/LCSYS.2024.3411509

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 letter addresses the problem of global exponential stability analysis of the origin of continuous-time Continuous Piecewise Affine (CPWA) systems. The stability analysis in this letter considers Piecewise Quadratic (PWQ) Lyapunov Functions (LF) and a ramp-based implicit representation of PWA systems. Sufficient convex stability conditions are obtained in the form of a Semidefinite Programming (SDP) problem. Two major benefits arise from the proposed results: i) the need for equality constraints to ensure the continuity of the LF across the boundaries of the sets of the partition is withdrawn; ii) there is no need to consider separate SDP conditions for each set of the partition, which simplifies the application of the conditions. The effectiveness of the proposed method is illustrated in numerical examples.

引用

页码：1649 / 1654

页数：6

共 50 条

[41] Absolute exponential stability of a class of continuous-time recurrent neural networks
Hu, SQ
Wang, J
IEEE TRANSACTIONS ON NEURAL NETWORKS, 2003, 14 (01): : 35 - 45
[42] Reachability of Standard and Fractional Continuous-Time Systems with Piecewise Constant Inputs
Rogowski, Krzysztof
CHALLENGES IN AUTOMATION, ROBOTICS AND MEASUREMENT TECHNIQUES, 2016, 440 : 341 - 349
[43] H∞ controller synthesis of uncertain piecewise continuous-time linear systems
Zhu, Y
Li, DQ
Feng, G
IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS, 2005, 152 (05): : 513 - 519
[44] Adaptive identification of continuous-time switched linear and piecewise linear systems
Kersting, Stefan
Buss, Martin
2014 EUROPEAN CONTROL CONFERENCE (ECC), 2014, : 31 - 36
[45] MPC for continuous piecewise-affine systems
De Schutter, B
van den Boom, TJJ
SYSTEMS & CONTROL LETTERS, 2004, 52 (3-4) : 179 - 192
[46] Stabilization of rank-deficient continuous-time switched affine systems
Egidio, Lucas N.
Deaecto, Grace S.
Jungers, Raphael M.
AUTOMATICA, 2022, 143
[47] On observer design for a class of continuous-time affine switched or switching systems
Menini, Laura
Possieri, Corrado
Tornambe, Antonio
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 6234 - 6239
[48] Static output feedback control for uncertain Roesser-type continuous-time two-dimensional piecewise affine systems
Wang, Meng
Qiu, Jianbin
Yan, Huaicheng
Li, Zhichen
Li, Yue
SCIENCE CHINA-INFORMATION SCIENCES, 2022, 65 (11)
[49] Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks
Hu, SQ
Wang, J
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (05) : 802 - 807
[50] An exponential continuous-time GARCH process
Haug, Stephan
Czado, Claudia
JOURNAL OF APPLIED PROBABILITY, 2007, 44 (04) : 960 - 976

← 1 2 3 4 5 →