This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results.
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October 2015
Research-Article
Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties
S. Dharani,
S. Dharani
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
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R. Rakkiyappan,
R. Rakkiyappan
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Search for other works by this author on:
Jinde Cao
Jinde Cao
Department of Mathematics and
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Search for other works by this author on:
S. Dharani
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
R. Rakkiyappan
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Jinde Cao
Department of Mathematics and
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 15, 2014; final manuscript received June 5, 2015; published online July 21, 2015. Assoc. Editor: Umesh Vaidya.
J. Dyn. Sys., Meas., Control. Oct 2015, 137(10): 101008
Published Online: July 21, 2015
Article history
Received:
August 15, 2014
Revision Received:
June 5, 2015
Citation
Dharani, S., Rakkiyappan, R., and Cao, J. (July 21, 2015). "Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties." ASME. J. Dyn. Sys., Meas., Control. October 2015; 137(10): 101008. https://doi.org/10.1115/1.4030800
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