Nguyen, Dung Tien and Mao, Xuerong and Yin, G. and Yuan, Chenggui
(2012)
*Stability of singular jump-linear systems with a large state space : a two-time-scale approach.*
The Australian and New Zealand Industrial and Applied Mathematics Journal, 52 (4).
pp. 372-390.

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## Abstract

This paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view.

Item type: | Article |
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ID code: | 41332 |

Keywords: | singular system, stabiity, two-time-scale approach, Probabilities. Mathematical statistics, Mathematics (miscellaneous) |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 03 Oct 2012 12:28 |

Last modified: | 15 Apr 2015 11:10 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/41332 |

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