Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations

In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results.

[1]  V. Hutson APPLIED THEORY OF FUNCTIONAL DIFFERENTIAL EDUQTIONS , 1995 .

[2]  Ju H. Park,et al.  Matrix Inequality Approach to a Novel Stability Criterion for Time-Delay Systems with Nonlinear Uncertainties , 2005 .

[3]  Ju H. Park,et al.  Robust stabilization of uncertain systems with delays in control input: a matrix inequality approach , 2006, Appl. Math. Comput..

[4]  Vladimir L. Kharitonov,et al.  On the stability of linear systems with uncertain delay , 2003, IEEE Trans. Autom. Control..

[5]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Ju H. Park,et al.  Exponential stability of uncertain dynamic systems including state delay , 2006, Appl. Math. Lett..

[7]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[8]  Ju H. Park,et al.  Controlling uncertain neutral dynamic systems with delay in control input , 2005 .

[9]  G. Hu,et al.  Some simple criteria for stability of neutral delay-differential systems , 1996 .

[10]  Shengyuan Xu,et al.  New Exponential Estimates for Time-Delay Systems , 2006, IEEE Transactions on Automatic Control.

[11]  Oh-Min Kwon,et al.  Robust H∞ Filtering for Uncertain Time-Delay Systems: Matrix Inequality Approach , 2006 .

[12]  J. H. Park,et al.  Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach , 2006 .

[13]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[14]  D. Yue,et al.  Guaranteed cost control of linear systems over networks with state and input quantisations , 2006 .

[15]  J. H. Park,et al.  Asymptotic Stability of Neutral Systems with Multiple Delays , 1999 .

[16]  Shaosheng Zhou,et al.  On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations , 2008 .

[17]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[18]  Ju H. Park,et al.  Novel stability criterion of time delay systems with nonlinear uncertainties , 2005, Appl. Math. Lett..

[19]  James Lam,et al.  Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations , 2000, Int. J. Syst. Sci..

[20]  Jinde Cao,et al.  Global asymptotic stability of neural networks with transmission delays , 2000, Int. J. Syst. Sci..

[21]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[22]  J. Hale Theory of Functional Differential Equations , 1977 .

[23]  Ju H. Park,et al.  On improved delay-dependent robust control for uncertain time-delay systems , 2004, IEEE Transactions on Automatic Control.

[24]  Z. Zuo,et al.  New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations , 2006 .

[25]  Wim Michiels,et al.  Stabilization of time-delay systems with a Controlled time-varying delay and applications , 2005, IEEE Transactions on Automatic Control.

[26]  D. Yue,et al.  Delay dependent stability of neutral systems with time delay: an LMI approach , 2003 .

[27]  Qing-Guo Wang,et al.  An Improved Hα Filter Design for Systems With Time-Varying Interval Delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.