A new procedure for determining the asymptotic stability with probability one of random-time-delay-controlled quasi-integrable Hamiltonian systems is proposed. Such a system is formulated as continuous–discrete hybrid system and the random time delay is modeled as a Markov jump process. A three-step approximation is taken to simplify such hybrid system: (i) the randomly periodic approximate solution property of the system is used to convert the random time delay control into the control without time delay but with delay time as parameter; (ii) a limit theorem is used to transform the hybrid system with Markov jump parameter into one without jump parameter; and (iii) the stochastic averaging method for quasi-integrable Hamiltonian systems is applied to reduce the system into a set of averaged Itô stochastic differential equations. An approximate expression for the largest Lyapunov exponent of the system is derived from the linearized averaged Itô equations and the necessary and sufficient condition for the asymptotic stability with probability one of the system is obtained. The application and effectiveness of the proposed procedure are demonstrated by using an example of stochastically driven two-degrees-of-freedom networked control system (NCS) with random time delay.
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September 2016
Research-Article
Asymptotic Stability With Probability One of Random-Time-Delay-Controlled Quasi-Integrable Hamiltonian Systems
R. H. Huan,
R. H. Huan
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Search for other works by this author on:
W. Q. Zhu,
W. Q. Zhu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Search for other works by this author on:
R. C. Hu,
R. C. Hu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Search for other works by this author on:
Z. G. Ying
Z. G. Ying
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Search for other works by this author on:
R. H. Huan
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
W. Q. Zhu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
R. C. Hu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Z. G. Ying
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and Smart
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 21, 2016; final manuscript received June 16, 2016; published online July 4, 2016. Editor: Yonggang Huang.
J. Appl. Mech. Sep 2016, 83(9): 091009 (8 pages)
Published Online: July 4, 2016
Article history
Received:
April 21, 2016
Revised:
June 16, 2016
Citation
Huan, R. H., Zhu, W. Q., Hu, R. C., and Ying, Z. G. (July 4, 2016). "Asymptotic Stability With Probability One of Random-Time-Delay-Controlled Quasi-Integrable Hamiltonian Systems." ASME. J. Appl. Mech. September 2016; 83(9): 091009. https://doi.org/10.1115/1.4033944
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