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Research Papers

Stochastic Sampled-Data Control for H Stabilization of Transport Reaction Systems

[+] Author and Article Information
R. Rakkiyappan

Department of Mathematics,
Bharathiar University,
Coimbatore 641 046,
Tamil Nadu, India
e-mail: rakkigru@gmail.com

S. Dharani

Department of Mathematics,
Bharathiar University,
Coimbatore 641 046,
Tamil Nadu, India
e-mail: sdharanimails@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 4, 2014; final manuscript received February 17, 2015; published online April 24, 2015. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 137(8), 081009 (Aug 01, 2015) (12 pages) Paper No: DS-14-1005; doi: 10.1115/1.4030087 History: Received January 04, 2014; Revised February 17, 2015; Online April 24, 2015

This paper investigates the problem of stochastic sampled-data H control for a class of parabolic systems governed by one-dimensional semilinear transport reaction systems with external disturbances. A sampled-data controller design is developed by introducing the time-varying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampled-data control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger’s inequality. With this new approach, sufficient conditions that guarantee the asymptotic mean-square stabilization of the considered systems and the L2-gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software.

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Figures

Grahic Jump Location
Fig. 1

Solution of Eq. (12) under the Dirichlet boundary condition

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