An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.

[1]  C. Lien.  Guaranteed Cost Observer–Based Controls for a Class of Uncertain Neutral Time-Delay Systems , 2005 .

[2]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

[3]  Ju H. Park.  Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties , 2001 .

[4]  Vu Ngoc Phat,et al.  Robust Stabilization of Linear Systems with Delayed State and Control , 2009 .

[5]  J. D. Chen,et al.  Delay-Dependent Nonfragile H∞ Observer-Based Control for Neutral Systems with Time Delays in the State and Control Input , 2009 .

[6]  Ju H. Park,et al.  On new stability criterion for delay-differential systems of neutral type , 2005, Appl. Math. Comput..

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

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

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

[10]  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..

[11]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

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

[13]  Firdaus E. Udwadia,et al.  Time-Delayed Positive Velocity Feedback Control Design for Active Control of Structures , 2006 .

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

[15]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[16]  Ju H. Park,et al.  On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays , 2008, Appl. Math. Comput..

[17]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

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

[19]  Ju H. Park,et al.  A note on stability of neutral delay-differential systems , 1999 .

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

[21]  C. Lien.  Delay-dependent stability criteria for uncertain neutral systems with multiple time-varying delays via LMI approach , 2005 .

[22]  D. Peaucelle,et al.  Stability of Time-Delay Systems with Non-Small Delay , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[23]  Mohammad Hosseini,et al.  Robust control of uncertain systems with time varying delays in control input , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).