Robust integral sliding mode control for Markovian jump systems: A singular system approach

Nasibeh Zohrabi; Amir Hossein Abolmasoumi; Hamid Reza Momeni; Sherif Abdelwahed

doi:10.1109/ACC.2016.7526811

Robust integral sliding mode control for Markovian jump systems: A singular system approach

Nasibeh Zohrabi, Amir Hossein Abolmasoumi, Hamid Reza Momeni, Sherif Abdelwahed

Penn State Brandywine

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

3 Scopus citations

Abstract

In this paper, an integral-type sliding mode controller is designed for continuous-time Markovian jump systems based on a singular system approach. The system's dynamical equations include an unknown function denoting the nonlinear uncertainty. The regularity, non-impulsiveness and stochastic stability of the resulting Markovian jump singular system are guaranteed by a new sufficient conditions in terms of strict linear matrix inequalities (LMIs). As a result, stochastic admissibility for sliding mode dynamics is assured. Then, a sliding mode control law is designed such that the closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Original language	English (US)
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7213-7218
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7526811
State	Published - Jul 28 2016
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Other

Other	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	7/6/16 → 7/8/16

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

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10.1109/ACC.2016.7526811

Cite this

Zohrabi, N., Abolmasoumi, A. H., Momeni, H. R., & Abdelwahed, S. (2016). Robust integral sliding mode control for Markovian jump systems: A singular system approach. In 2016 American Control Conference, ACC 2016 (pp. 7213-7218). Article 7526811 (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7526811

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title = "Robust integral sliding mode control for Markovian jump systems: A singular system approach",

abstract = "In this paper, an integral-type sliding mode controller is designed for continuous-time Markovian jump systems based on a singular system approach. The system's dynamical equations include an unknown function denoting the nonlinear uncertainty. The regularity, non-impulsiveness and stochastic stability of the resulting Markovian jump singular system are guaranteed by a new sufficient conditions in terms of strict linear matrix inequalities (LMIs). As a result, stochastic admissibility for sliding mode dynamics is assured. Then, a sliding mode control law is designed such that the closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.",

author = "Nasibeh Zohrabi and Abolmasoumi, {Amir Hossein} and Momeni, {Hamid Reza} and Sherif Abdelwahed",

note = "Publisher Copyright: {\textcopyright} 2016 American Automatic Control Council (AACC).; 2016 American Control Conference, ACC 2016 ; Conference date: 06-07-2016 Through 08-07-2016",

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doi = "10.1109/ACC.2016.7526811",

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Zohrabi, N, Abolmasoumi, AH, Momeni, HR & Abdelwahed, S 2016, Robust integral sliding mode control for Markovian jump systems: A singular system approach. in 2016 American Control Conference, ACC 2016., 7526811, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 7213-7218, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7526811

Robust integral sliding mode control for Markovian jump systems: A singular system approach. / Zohrabi, Nasibeh; Abolmasoumi, Amir Hossein; Momeni, Hamid Reza et al.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 7213-7218 7526811 (Proceedings of the American Control Conference; Vol. 2016-July).

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

TY - GEN

T1 - Robust integral sliding mode control for Markovian jump systems

T2 - 2016 American Control Conference, ACC 2016

AU - Zohrabi, Nasibeh

AU - Abolmasoumi, Amir Hossein

AU - Momeni, Hamid Reza

AU - Abdelwahed, Sherif

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N2 - In this paper, an integral-type sliding mode controller is designed for continuous-time Markovian jump systems based on a singular system approach. The system's dynamical equations include an unknown function denoting the nonlinear uncertainty. The regularity, non-impulsiveness and stochastic stability of the resulting Markovian jump singular system are guaranteed by a new sufficient conditions in terms of strict linear matrix inequalities (LMIs). As a result, stochastic admissibility for sliding mode dynamics is assured. Then, a sliding mode control law is designed such that the closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

AB - In this paper, an integral-type sliding mode controller is designed for continuous-time Markovian jump systems based on a singular system approach. The system's dynamical equations include an unknown function denoting the nonlinear uncertainty. The regularity, non-impulsiveness and stochastic stability of the resulting Markovian jump singular system are guaranteed by a new sufficient conditions in terms of strict linear matrix inequalities (LMIs). As a result, stochastic admissibility for sliding mode dynamics is assured. Then, a sliding mode control law is designed such that the closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 6 July 2016 through 8 July 2016

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Robust integral sliding mode control for Markovian jump systems: A singular system approach

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