• Previous Article
    An alternating direction method for solving a class of inverse semi-definite quadratic programming problems
  • JIMO Home
  • This Issue
  • Next Article
    Subgradient-based neural network for nonconvex optimization problems in support vector machines with indefinite kernels
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

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.
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
References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

The MathWorks, Inc, 1995. Google Scholar

[8]

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

[9]

Journal of Industrial and Management Optimization, 10 (2014), 413-441.  Google Scholar

[10]

Control Engineering. Birkhäuser/Springer, New York, 2013.  Google Scholar

[11]

Journal of Optimization Theory and Applications, 137 (2008), 521-532. doi: 10.1007/s10957-008-9357-7.  Google Scholar

[12]

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

[13]

Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043-1049. doi: 10.1016/j.cnsns.2008.03.010.  Google Scholar

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

Journal of the Franklin Institute, 348 (2011), 331-352. doi: 10.1016/j.jfranklin.2010.12.001.  Google Scholar

[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

show all references

References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

The MathWorks, Inc, 1995. Google Scholar

[8]

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

[9]

Journal of Industrial and Management Optimization, 10 (2014), 413-441.  Google Scholar

[10]

Control Engineering. Birkhäuser/Springer, New York, 2013.  Google Scholar

[11]

Journal of Optimization Theory and Applications, 137 (2008), 521-532. doi: 10.1007/s10957-008-9357-7.  Google Scholar

[12]

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

[13]

Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043-1049. doi: 10.1016/j.cnsns.2008.03.010.  Google Scholar

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

Journal of the Franklin Institute, 348 (2011), 331-352. doi: 10.1016/j.jfranklin.2010.12.001.  Google Scholar

[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

[1]

K. Aruna Sakthi, A. Vinodkumar. Stabilization on input time-varying delay for linear switched systems with truncated predictor control. Numerical Algebra, Control & Optimization, 2020, 10 (2) : 237-247. doi: 10.3934/naco.2019050

[2]

Shu Zhang, Jian Xu. Time-varying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 653-668. doi: 10.3934/dcdsb.2011.16.653

[3]

Peter Giesl. Construction of a finite-time Lyapunov function by meshless collocation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2387-2412. doi: 10.3934/dcdsb.2012.17.2387

[4]

Roberta Fabbri, Russell Johnson, Sylvia Novo, Carmen Núñez. On linear-quadratic dissipative control processes with time-varying coefficients. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 193-210. doi: 10.3934/dcds.2013.33.193

[5]

Le Viet Cuong, Thai Son Doan. Assignability of dichotomy spectra for discrete time-varying linear control systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3597-3607. doi: 10.3934/dcdsb.2020074

[6]

Sanjeeva Balasuriya. Uncertainty in finite-time Lyapunov exponent computations. Journal of Computational Dynamics, 2020, 7 (2) : 313-337. doi: 10.3934/jcd.2020013

[7]

Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control & Related Fields, 2015, 5 (4) : 721-742. doi: 10.3934/mcrf.2015.5.721

[8]

Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098

[9]

Mokhtari Yacine. Boundary controllability and boundary time-varying feedback stabilization of the 1D wave equation in non-cylindrical domains. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021004

[10]

Carlos Nonato, Manoel Jeremias dos Santos, Carlos Raposo. Dynamics of Timoshenko system with time-varying weight and time-varying delay. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021053

[11]

Li-Min Wang, Jing-Xian Yu, Jia Shi, Fu-Rong Gao. Delay-range dependent $H_\infty$ control for uncertain 2D-delayed systems. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 11-23. doi: 10.3934/naco.2015.5.11

[12]

Yangzi Hu, Fuke Wu. The improved results on the stochastic Kolmogorov system with time-varying delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1481-1497. doi: 10.3934/dcdsb.2015.20.1481

[13]

Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693

[14]

Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023

[15]

Arno Berger. On finite-time hyperbolicity. Communications on Pure & Applied Analysis, 2011, 10 (3) : 963-981. doi: 10.3934/cpaa.2011.10.963

[16]

M. S. Mahmoud, P. Shi, Y. Shi. $H_\infty$ and robust control of interconnected systems with Markovian jump parameters. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 365-384. doi: 10.3934/dcdsb.2005.5.365

[17]

Jamal Mrazgua, El Houssaine Tissir, Mohamed Ouahi. Frequency domain $ H_{\infty} $ control design for active suspension systems. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021036

[18]

Nguyen H. Sau, Vu N. Phat. LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback. Journal of Industrial & Management Optimization, 2018, 14 (2) : 583-596. doi: 10.3934/jimo.2017061

[19]

Markus Dick, Martin Gugat, Günter Leugering. A strict $H^1$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 225-244. doi: 10.3934/naco.2011.1.225

[20]

Martin Gugat, Günter Leugering, Ke Wang. Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $H^2$-lyapunov function. Mathematical Control & Related Fields, 2017, 7 (3) : 419-448. doi: 10.3934/mcrf.2017015

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]