Necessary Conditions for the Stability of One Delay Systems: A Lyapunov Matrix Approach

Abstract Necessary conditions for the exponential stability of one delay linear systems expressed in terms of the Lyapunov matrix of the system are proved. The effectiveness of the proposed conditions is shown in illustrative examples.

[1]  Sabine Mondié,et al.  Tuning the leading roots of a second order DC servomotor with proportional retarded control , 2010 .

[2]  J. Louisell.  Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system , 1998 .

[3]  V. Kharitonov,et al.  Robust stability of time-delay systems , 1994, IEEE Trans. Autom. Control..

[4]  R. Datko.  AN ALGORITHM FOR COMPUTING LIAPUNOV FUNCTIONALS FOR SOME DIFFERENTIAL-DIFFERENCE EQUATIONS , 1972 .

[5]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[6]  Keqin Gu,et al.  On the fragility of PI controllers for time-delay SISO systems , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[7]  Vladimir L. Kharitonov,et al.  Lyapunov matrices for a class of time delay systems , 2006, Syst. Control. Lett..

[8]  Vladimir L. Kharitonov,et al.  Lyapunov matrices for time delay systems , 2005, 2005 2nd International Conference on Electrical and Electronics Engineering.

[9]  Sabine Mondié,et al.  Some necessary conditions for the exponential stability of one delay systems , 2011, 2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control.

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

[11]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii Approach to Robust Stability of Time Delay Systems , 2001 .

[12]  Iu M Repin.  Quadratic liapunov functionals for systems with delay , 1965 .

[13]  Matrix convex directions for time delay systems , 2003 .

[14]  Sabine Mondié,et al.  Instability conditions for linear time delay systems: a Lyapunov matrix function approach , 2011, Int. J. Control.

[15]  E. Infante,et al.  A Liapunov Functional for a Matrix Difference-Differential Equation, , 1978 .

[16]  Sabine Mondié,et al.  Assessing the exact stability region of the single-delay scalar equation via its Lyapunov function , 2012, IMA J. Math. Control. Inf..

[17]  Huang Wenzhang,et al.  Generalization of Liapunov's theorem in a linear delay system , 1989 .