### Abstract

In this paper, we study several qualitative properties for a class of switched systems composed of several subsystems, where each subsystem's vector field is composed of a linear time-invariant part and a nonlinear norm-bounded perturbation part. It is assumed that the linear subsystem matrices are commutative pairwise, and there exists a linear convex stable combination of unstable linear subsystem matrices. First, in the case of no perturbations, we propose a switching law under which the entire switched system is globally exponentially stable. In the switching law, Hurwitz stable sub-systems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. Secondly, under the same switching law, we analyze qualitative property of the switched system in the case where nonlinear norm-bounded perturbations exist. Some numerical examples are given in the paper to demonstrate the results.

Original language | English |
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Title of host publication | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |

Editors | S. Chunlin, S. Chunlin |

Pages | 139-144 |

Number of pages | 6 |

Publication status | Published - 2000 |

Externally published | Yes |

Event | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement - Guilin Duration: 2000 Jul 9 → 2000 Jul 12 |

### Other

Other | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |
---|---|

City | Guilin |

Period | 00/7/9 → 00/7/12 |

### Keywords

- Commutative pairwise
- Exponential stability
- Nonlinear perturbations
- Switched system
- Switching law

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the 4th Asia-Pacific Conference on Control and Measurement*(pp. 139-144)

**Qualitative analysis for a class of switched systems.** / Zhai, Guisheng; Yasuda, Kazunori.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 4th Asia-Pacific Conference on Control and Measurement.*pp. 139-144, Proceedings of the 4th Asia-Pacific Conference on Control and Measurement, Guilin, 00/7/9.

}

TY - GEN

T1 - Qualitative analysis for a class of switched systems

AU - Zhai, Guisheng

AU - Yasuda, Kazunori

PY - 2000

Y1 - 2000

N2 - In this paper, we study several qualitative properties for a class of switched systems composed of several subsystems, where each subsystem's vector field is composed of a linear time-invariant part and a nonlinear norm-bounded perturbation part. It is assumed that the linear subsystem matrices are commutative pairwise, and there exists a linear convex stable combination of unstable linear subsystem matrices. First, in the case of no perturbations, we propose a switching law under which the entire switched system is globally exponentially stable. In the switching law, Hurwitz stable sub-systems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. Secondly, under the same switching law, we analyze qualitative property of the switched system in the case where nonlinear norm-bounded perturbations exist. Some numerical examples are given in the paper to demonstrate the results.

AB - In this paper, we study several qualitative properties for a class of switched systems composed of several subsystems, where each subsystem's vector field is composed of a linear time-invariant part and a nonlinear norm-bounded perturbation part. It is assumed that the linear subsystem matrices are commutative pairwise, and there exists a linear convex stable combination of unstable linear subsystem matrices. First, in the case of no perturbations, we propose a switching law under which the entire switched system is globally exponentially stable. In the switching law, Hurwitz stable sub-systems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. Secondly, under the same switching law, we analyze qualitative property of the switched system in the case where nonlinear norm-bounded perturbations exist. Some numerical examples are given in the paper to demonstrate the results.

KW - Commutative pairwise

KW - Exponential stability

KW - Nonlinear perturbations

KW - Switched system

KW - Switching law

UR - http://www.scopus.com/inward/record.url?scp=0034590285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034590285&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0034590285

SN - 7801346955

SP - 139

EP - 144

BT - Proceedings of the 4th Asia-Pacific Conference on Control and Measurement

A2 - Chunlin, S.

A2 - Chunlin, S.

ER -