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need for equality constraints to ensure the continuity of the LF across the boundaries of the sets of the partition is withdrawn; ii) there is no need to consider separate SDP conditions for each set of the partition, which simplifies the application of the conditions.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

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