On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Zidong Wang; Hong Qiao; K. J. Burnham

doi:10.1109/9.995042

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Zidong Wang
, Hong Qiao
, K. J. Burnham

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

264 Citations (Scopus)

Abstract

In this note, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulations.
© 2002 IEEE

Original language	English
Pages (from-to)	640-646
Journal	IEEE Transactions on Automatic Control
Volume	47
Issue number	4
DOIs	https://doi.org/10.1109/9.995042
Publication status	Published - Apr 2002
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

The work of Z. Wang was supported in part by the City University of Hong Kong, the University of Kaiserslautern of Germany, and the Alexander von Humboldt Foundation of Germany.

Research Keywords

Bilinear systems
Linear matrix inequalities (LMIs)
Markovian jump
Stochastic exponential stability
Time-delay
Uncertainty

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title = "On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters",

abstract = "In this note, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulations. {\textcopyright} 2002 IEEE",

keywords = "Bilinear systems, Linear matrix inequalities (LMIs), Markovian jump, Stochastic exponential stability, Time-delay, Uncertainty",

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AU - Qiao, Hong

AU - Burnham, K. J.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - In this note, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulations. © 2002 IEEE

AB - In this note, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulations. © 2002 IEEE

KW - Bilinear systems

KW - Linear matrix inequalities (LMIs)

KW - Markovian jump

KW - Stochastic exponential stability

KW - Time-delay

KW - Uncertainty

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DO - 10.1109/9.995042

M3 - RGC 21 - Publication in refereed journal

SN - 0018-9286

VL - 47

SP - 640

EP - 646

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

ER -

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

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