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Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback
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 |
References:
[1] |
F. Amato, M. Ariola and C. Cosentino, Finite-time stabilization via dynamic output feedback,, Automatica, 42 (2006), 337.
doi: 10.1016/j.automatica.2005.09.007. |
[2] |
F. Amato, G. De Tommasi and A. Pironti, Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems,, Automatica, 49 (2013), 2546.
doi: 10.1016/j.automatica.2013.04.004. |
[3] |
E. K. Boukas, Static output feedback control for stochastic hybrid systems: LMI approach,, Automatica, 42 (2006), 183.
doi: 10.1016/j.automatica.2005.08.012. |
[4] |
S. Boyd, L. El. Ghaoui and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory,, SIAM, (1994).
doi: 10.1137/1.9781611970777. |
[5] |
P. Dorato, Short time stability in linear time-varying systems,, In Proc IRE Int Convention Record, 4 (1961), 83. Google Scholar |
[6] |
E. Fridman and U. Shaked, Delay-dependent stability and $H_{\infty}$control: constant and time-varying delays,, International Journal of Control, 76 (2003), 48.
doi: 10.1080/0020717021000049151. |
[7] |
P. Gahinet, A. Nemirovskii, A. J. Laub and M. Chilali, LMI Control Toolbox For use with MATLAB,, The MathWorks, (1995). Google Scholar |
[8] |
G. Garcia, S. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems,, IEEE Transactions on Automatic Control, 54 (2009), 364.
doi: 10.1109/TAC.2008.2008325. |
[9] |
L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays,, Journal of Industrial and Management Optimization, 10 (2014), 413.
|
[10] |
V. Kharitonov, Time-Delay Systems: Lyapunov Functionals and Matrices,, Control Engineering. Birkhäuser/Springer, (2013).
|
[11] |
O. M. Kwon, J. H. Park and S. M. Lee, Exponential stability for uncertain dynamic systems with time-varying delays: LMI optimization approach,, Journal of Optimization Theory and Applications, 137 (2008), 521.
doi: 10.1007/s10957-008-9357-7. |
[12] |
H. Liu, Y. Shen and X. Zhao, Delay-dependent observer-based $H_\infty$ finite-time control for switched systems with time-varying delay,, Nonlinear Analysis: Hybrid Systems, 6 (2012), 885.
doi: 10.1016/j.nahs.2012.03.001. |
[13] |
Q. Y. Meng and Y. J Shen, Finite-time $H_\infty$ control for linear continuous system with norm-bounded disturbance,, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043.
doi: 10.1016/j.cnsns.2008.03.010. |
[14] |
E. Moulay, M. Dambrine, N. Yeganefar and W. Perruquetti, Finite-time stability and stabilization of time-delay systems,, Systems and Control Letters, 57 (2008), 561.
doi: 10.1016/j.sysconle.2007.12.002. |
[15] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays,, Journal of Optimization Theory and Applications, 151 (2011), 100.
doi: 10.1007/s10957-011-9858-7. |
[16] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays,, Journal of Optimization Theory and Applications, 151 (2011), 100.
doi: 10.1007/s10957-011-9858-7. |
[17] |
A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems,, Automatica, 49 (2013), 2860.
doi: 10.1016/j.automatica.2013.05.030. |
[18] |
L. Wu, J. Lam and C. Wang, Robust $H_{\infty}$ dynamic output feedback control for 2D linear parameter-varying systems,, IMA journal of mathematical control and information, 26 (2009), 23.
doi: 10.1093/imamci/dnm028. |
[19] |
Z. Xiang, Y. N. Sun and M. S. Mahmoud, Robust finite-time $H_\infty$ control for a class of uncertain switched neutral systems,, Communications in Nonlinear Science Numerical Simulations, 17 (2012), 1766.
doi: 10.1016/j.cnsns.2011.09.022. |
[20] |
W. Xiang and J. Xiao, $H_{\infty}$ finite-time control for nonlinear switched discrete-time systems with norm-bounded disturbance,, Journal of the Franklin Institute, 348 (2011), 331.
doi: 10.1016/j.jfranklin.2010.12.001. |
[21] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach,, Journal of Industrial and Management Optimization, 5 (2009), 153.
doi: 10.3934/jimo.2009.5.153. |
[22] |
Y. Zhang, C. Liu and X. Mu, Robust finite-time $H_\infty$ control of singular stochastic systems via static output feedback,, Applied Mathematics and Computation, 218 (2012), 5629.
doi: 10.1016/j.amc.2011.11.057. |
show all references
References:
[1] |
F. Amato, M. Ariola and C. Cosentino, Finite-time stabilization via dynamic output feedback,, Automatica, 42 (2006), 337.
doi: 10.1016/j.automatica.2005.09.007. |
[2] |
F. Amato, G. De Tommasi and A. Pironti, Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems,, Automatica, 49 (2013), 2546.
doi: 10.1016/j.automatica.2013.04.004. |
[3] |
E. K. Boukas, Static output feedback control for stochastic hybrid systems: LMI approach,, Automatica, 42 (2006), 183.
doi: 10.1016/j.automatica.2005.08.012. |
[4] |
S. Boyd, L. El. Ghaoui and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory,, SIAM, (1994).
doi: 10.1137/1.9781611970777. |
[5] |
P. Dorato, Short time stability in linear time-varying systems,, In Proc IRE Int Convention Record, 4 (1961), 83. Google Scholar |
[6] |
E. Fridman and U. Shaked, Delay-dependent stability and $H_{\infty}$control: constant and time-varying delays,, International Journal of Control, 76 (2003), 48.
doi: 10.1080/0020717021000049151. |
[7] |
P. Gahinet, A. Nemirovskii, A. J. Laub and M. Chilali, LMI Control Toolbox For use with MATLAB,, The MathWorks, (1995). Google Scholar |
[8] |
G. Garcia, S. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems,, IEEE Transactions on Automatic Control, 54 (2009), 364.
doi: 10.1109/TAC.2008.2008325. |
[9] |
L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays,, Journal of Industrial and Management Optimization, 10 (2014), 413.
|
[10] |
V. Kharitonov, Time-Delay Systems: Lyapunov Functionals and Matrices,, Control Engineering. Birkhäuser/Springer, (2013).
|
[11] |
O. M. Kwon, J. H. Park and S. M. Lee, Exponential stability for uncertain dynamic systems with time-varying delays: LMI optimization approach,, Journal of Optimization Theory and Applications, 137 (2008), 521.
doi: 10.1007/s10957-008-9357-7. |
[12] |
H. Liu, Y. Shen and X. Zhao, Delay-dependent observer-based $H_\infty$ finite-time control for switched systems with time-varying delay,, Nonlinear Analysis: Hybrid Systems, 6 (2012), 885.
doi: 10.1016/j.nahs.2012.03.001. |
[13] |
Q. Y. Meng and Y. J Shen, Finite-time $H_\infty$ control for linear continuous system with norm-bounded disturbance,, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043.
doi: 10.1016/j.cnsns.2008.03.010. |
[14] |
E. Moulay, M. Dambrine, N. Yeganefar and W. Perruquetti, Finite-time stability and stabilization of time-delay systems,, Systems and Control Letters, 57 (2008), 561.
doi: 10.1016/j.sysconle.2007.12.002. |
[15] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays,, Journal of Optimization Theory and Applications, 151 (2011), 100.
doi: 10.1007/s10957-011-9858-7. |
[16] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays,, Journal of Optimization Theory and Applications, 151 (2011), 100.
doi: 10.1007/s10957-011-9858-7. |
[17] |
A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems,, Automatica, 49 (2013), 2860.
doi: 10.1016/j.automatica.2013.05.030. |
[18] |
L. Wu, J. Lam and C. Wang, Robust $H_{\infty}$ dynamic output feedback control for 2D linear parameter-varying systems,, IMA journal of mathematical control and information, 26 (2009), 23.
doi: 10.1093/imamci/dnm028. |
[19] |
Z. Xiang, Y. N. Sun and M. S. Mahmoud, Robust finite-time $H_\infty$ control for a class of uncertain switched neutral systems,, Communications in Nonlinear Science Numerical Simulations, 17 (2012), 1766.
doi: 10.1016/j.cnsns.2011.09.022. |
[20] |
W. Xiang and J. Xiao, $H_{\infty}$ finite-time control for nonlinear switched discrete-time systems with norm-bounded disturbance,, Journal of the Franklin Institute, 348 (2011), 331.
doi: 10.1016/j.jfranklin.2010.12.001. |
[21] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach,, Journal of Industrial and Management Optimization, 5 (2009), 153.
doi: 10.3934/jimo.2009.5.153. |
[22] |
Y. Zhang, C. Liu and X. Mu, Robust finite-time $H_\infty$ control of singular stochastic systems via static output feedback,, Applied Mathematics and Computation, 218 (2012), 5629.
doi: 10.1016/j.amc.2011.11.057. |
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