Delay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The pro- posed methods employ a suitable Lyapunov-Krasovskii's functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results. Keywords—Neutral systems; Time-delay; Stability; Lyapunov method; LMI.

[1]  Wei Wang,et al.  Delay and its time-derivative dependent robust stability of neutral control system , 2007, Appl. Math. Comput..

[2]  Maurício C. de Oliveira,et al.  Investigating duality on stability conditions , 2004, Syst. Control. Lett..

[3]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[4]  Frédéric Gouaisbaut,et al.  An augmented model for robust stability analysis of time-varying delay systems , 2009, Int. J. Control.

[5]  Jin-Hua She,et al.  New delay-dependent stability criteria and stabilizing method for neutral systems , 2004, IEEE Trans. Autom. Control..

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

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

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

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

[10]  Shengyuan Xu,et al.  Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems , 2005 .

[11]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[12]  Bernard Brogliato,et al.  Force Measurement Time-Delays and Contact Instability Phenomenon , 1999, Eur. J. Control.

[13]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[14]  D. Yue,et al.  A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Haibo Wang,et al.  New stability analysis for linear neutral system via state matrix decomposition , 2009, Appl. Math. Comput..

[16]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

[18]  Dong Yue,et al.  A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model , 2004, Proceedings of the 2004 American Control Conference.

[19]  M. Parlakçi.  Extensively augmented Lyapunov functional approach for the stability of neutral time-delay systems , 2008 .

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

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

[22]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[23]  Ju H. Park,et al.  Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays , 2009, Appl. Math. Comput..

[24]  A. Bellen,et al.  Methods for linear systems of circuit delay differential equations of neutral type , 1999 .

[25]  Shengyuan Xu,et al.  Further results on delay‐dependent robust stability conditions of uncertain neutral systems , 2005 .

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

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