Refined discretized Lyapunov functional method for systems with multiple delays

A discretized Lyapunov functional method for systems with multiple delay is refined. The main ideas used are variable elimination and integral inequality. The resulting new stability criterion is simpler. Numerical examples indicate that the new method is much less conservative for a given discretization mesh. In most applications, it appears that a most coarse discretization mesh compatible with the delays is sufficient.

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

[2]  K. Gu Discretized LMI set in the stability problem of linear uncertain time-delay systems , 1997 .

[3]  Jean-Michel Dion,et al.  Stability and robust stability of time-delay systems: A guided tour , 1998 .

[4]  Vladimir L. Kharitonov,et al.  Robust stability analysis of time delay systems: A survey , 1999 .

[5]  K. Gu,et al.  Delay effects on stability: a survey , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  Keqin Gu Discretized Lyapunov functional for uncertain systems with multiple time-delay , 1999 .

[7]  Keqin Gu,et al.  Partial solution of LMI in stability problem of time-delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[8]  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).

[9]  K. Gu A further refinement of discretized Lyapunov functional method for the time-delay systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[10]  K. Gu,et al.  On robust stability of time-delay systems with norm-bounded uncertainty , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).