<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.</p></abstract>

This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

Department of Electronic Systems, Automation and Control Aalborg University, Fredrik Bajers Vej 7 C, 9220 Aalborg East, Denmark

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local...

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

Published Online: Jun 26, 2014

Page range: 341 - 355

Received: Apr 10, 2013

DOI: https://doi.org/10.2478/amcs-2014-0026

Keywords
stability, switched systems, hybrid systems, differential inclusions

© 2014 John Leth and Rafael Wisniewski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

Published Online: Jun 26, 2014

Page range: 341 - 355

Received: Apr 10, 2013

DOI: https://doi.org/10.2478/amcs-2014-0026

Keywordsstability, switched systems, hybrid systems, differential inclusions

© 2014 John Leth and Rafael Wisniewski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
stability, switched systems, hybrid systems, differential inclusions