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January  2016, 12(1): 303-315. doi: 10.3934/jimo.2016.12.303

Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback

Ta T.H. Trang 1, , Vu N. Phat 1, and  Adly Samir 2,

1. 

Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi 10307, Vietnam, Vietnam
2. 

Université de Limoges, Laboratoire XLIM, 123, avenue Albert Thomas, 87060 Limoges CEDEX, France

Received  November 2014 Revised  January 2015 Published  April 2015

This paper studies the robust finite-time $H_\infty$ control for a class of nonlinear systems with time-varying delay and disturbances via output feedback. Based on the Lyapunov functional method and a generalized Jensen integral inequality, novel delay-dependent conditions for the existence of output feedback controllers are established in terms of linear matrix inequalities (LMIs). The proposed conditions allow us to design the output feedback controllers which robustly stabilize the closed-loop system in the finite-time sense. An application to $H_\infty$ control of uncertain linear systems with interval time-varying delay is also given. A numerical example is given to illustrate the efficiency of the proposed method.
Keywords: time-varying delay, Finite-time stabilization, output feedback, Lyapunov function, $H_\infty$ control, linear matrix inequality..
Mathematics Subject Classification: Primary: 93D20, 34D20; Secondary: 37C7.
Citation: Ta T.H. Trang, Vu N. Phat, Adly Samir. Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 303-315. doi: 10.3934/jimo.2016.12.303
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show all references

References:
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Automatica, 42 (2006), 337-342. doi: 10.1016/j.automatica.2005.09.007.  Google Scholar

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Automatica, 49 (2013), 2546-2550. doi: 10.1016/j.automatica.2013.04.004.  Google Scholar

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Automatica, 42 (2006), 183-188. doi: 10.1016/j.automatica.2005.08.012.  Google Scholar

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SIAM, Philadelphia, PA, 1994. doi: 10.1137/1.9781611970777.  Google Scholar

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In Proc IRE Int Convention Record, 4 (1961), 83-87. Google Scholar

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International Journal of Control, 76 (2003), 48-60. doi: 10.1080/0020717021000049151.  Google Scholar

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The MathWorks, Inc, 1995. Google Scholar

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IEEE Transactions on Automatic Control, 54 (2009), 364-369. doi: 10.1109/TAC.2008.2008325.  Google Scholar

[9]

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[10]

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[11]

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[12]

Nonlinear Analysis: Hybrid Systems, 6 (2012), 885-898. doi: 10.1016/j.nahs.2012.03.001.  Google Scholar

[13]

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[14]

Systems and Control Letters, 57 (2008), 561-566. doi: 10.1016/j.sysconle.2007.12.002.  Google Scholar

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Journal of Optimization Theory and Applications,151 (2011), 100-120. doi: 10.1007/s10957-011-9858-7.  Google Scholar

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[17]

Automatica, 49 (2013), 2860-2866. doi: 10.1016/j.automatica.2013.05.030.  Google Scholar

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IMA journal of mathematical control and information, 26 (2009), 23-44. doi: 10.1093/imamci/dnm028.  Google Scholar

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Communications in Nonlinear Science Numerical Simulations, 17 (2012), 1766-1778. doi: 10.1016/j.cnsns.2011.09.022.  Google Scholar

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[21]

Journal of Industrial and Management Optimization, 5 (2009), 153-159. doi: 10.3934/jimo.2009.5.153.  Google Scholar

[22]

Applied Mathematics and Computation, 218 (2012), 5629-5640. doi: 10.1016/j.amc.2011.11.057.  Google Scholar

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