Stability for hybrid event systems

Bin Liu; David J. Hill

doi:10.1109/CDC.2012.6426599

Stability for hybrid event systems

Bin Liu^*, David J. Hill

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

This paper studies the stability of hybrid event systems (HES). By the partition of time set, we formulate the HES model which includes several special cases reported in the literature. Two types of stability notions (the first and the second stability) are proposed to reflect the effect on stability from hybrid events. A new stability analysis method called hybrid-event-time Lyapunov function (HTLF) approach is proposed for HES. A basic stability result is derived for HES. That is: a HES has the second asymptotic stability if and only if there exists a HTLF which is strictly decreasing and converges to zero. Moreover, by constructing HTLF and integrating the Razumikhin technique, the backward and forward HTLF-Razumikhin-type stability theorems are established. As applications, the results are then used to derive Razumikhin-type exponential stability theorems for impulsive HES with delays. Finally, one example is given to illustrate the results.

Original language	English
Article number	6426599
Pages (from-to)	6849-6854
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6426599
Publication status	Published - 2012
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 10 Dec 2012 → 13 Dec 2012

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title = "Stability for hybrid event systems",

abstract = "This paper studies the stability of hybrid event systems (HES). By the partition of time set, we formulate the HES model which includes several special cases reported in the literature. Two types of stability notions (the first and the second stability) are proposed to reflect the effect on stability from hybrid events. A new stability analysis method called hybrid-event-time Lyapunov function (HTLF) approach is proposed for HES. A basic stability result is derived for HES. That is: a HES has the second asymptotic stability if and only if there exists a HTLF which is strictly decreasing and converges to zero. Moreover, by constructing HTLF and integrating the Razumikhin technique, the backward and forward HTLF-Razumikhin-type stability theorems are established. As applications, the results are then used to derive Razumikhin-type exponential stability theorems for impulsive HES with delays. Finally, one example is given to illustrate the results.",

author = "Bin Liu and Hill, {David J.}",

year = "2012",

doi = "10.1109/CDC.2012.6426599",

language = "English",

pages = "6849--6854",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

}

TY - JOUR

T1 - Stability for hybrid event systems

AU - Liu, Bin

AU - Hill, David J.

PY - 2012

Y1 - 2012

N2 - This paper studies the stability of hybrid event systems (HES). By the partition of time set, we formulate the HES model which includes several special cases reported in the literature. Two types of stability notions (the first and the second stability) are proposed to reflect the effect on stability from hybrid events. A new stability analysis method called hybrid-event-time Lyapunov function (HTLF) approach is proposed for HES. A basic stability result is derived for HES. That is: a HES has the second asymptotic stability if and only if there exists a HTLF which is strictly decreasing and converges to zero. Moreover, by constructing HTLF and integrating the Razumikhin technique, the backward and forward HTLF-Razumikhin-type stability theorems are established. As applications, the results are then used to derive Razumikhin-type exponential stability theorems for impulsive HES with delays. Finally, one example is given to illustrate the results.

AB - This paper studies the stability of hybrid event systems (HES). By the partition of time set, we formulate the HES model which includes several special cases reported in the literature. Two types of stability notions (the first and the second stability) are proposed to reflect the effect on stability from hybrid events. A new stability analysis method called hybrid-event-time Lyapunov function (HTLF) approach is proposed for HES. A basic stability result is derived for HES. That is: a HES has the second asymptotic stability if and only if there exists a HTLF which is strictly decreasing and converges to zero. Moreover, by constructing HTLF and integrating the Razumikhin technique, the backward and forward HTLF-Razumikhin-type stability theorems are established. As applications, the results are then used to derive Razumikhin-type exponential stability theorems for impulsive HES with delays. Finally, one example is given to illustrate the results.

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U2 - 10.1109/CDC.2012.6426599

DO - 10.1109/CDC.2012.6426599

M3 - Conference article

AN - SCOPUS:84874284075

SN - 0743-1546

SP - 6849

EP - 6854

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

M1 - 6426599

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

Y2 - 10 December 2012 through 13 December 2012

ER -

Stability for hybrid event systems

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