Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients

The stability problem for systems with distributed delay is considered using discretized Lyapunov functional. The coefficients associated with the distributed delay are assumed to be piecewise constant, and the discretization mesh may be non-uniform. The resulting stability criteria are written in the form of linear matrix inequality. Numerical examples are also provided to illustrate the effectiveness of the method. The basic idea can be extended to a more general setting with more involved formulation.

[1]  W. Ergen.  Kinetics of the Circulating‐Fuel Nuclear Reactor , 1954 .

[2]  K. Cooke,et al.  Stability Conditions for Linear Retarded Functional Differential Equations , 1983 .

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

[4]  Marcel Abendroth,et al.  Biological delay systems: Linear stability theory , 1990 .

[5]  Bor-Sen Chen,et al.  Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach , 1991 .

[6]  K. Furuta,et al.  Memoryless stabilization of uncertain linear systems including time-varying state delays , 1992 .

[7]  C. Abdallah,et al.  Delayed Positive Feedback Can Stabilize Oscillatory Systems , 1993, 1993 American Control Conference.

[8]  A. Ivanov,et al.  Robust stability of systems with delayed feedback , 1994 .

[9]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[10]  L. Dugard,et al.  Delay-dependent stability of linear systems with delayed state: an LMI approach , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[11]  Jean-Pierre Richard,et al.  Stability of some systems with distributed delay , 1997 .

[12]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

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

[14]  Jean-Pierre Richard,et al.  Some Model Transformation for the Stability Study of Linear Systems With Delay , 1998 .

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

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

[17]  Keqin Gu,et al.  Stability of linear time-delay systems with block-diagonal uncertainty , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

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

[19]  Keqin Gu,et al.  A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems , 1999 .

[20]  Keqin Gu,et al.  Discretized Lyapunov functional for uncertain systems with multiple time-delay , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[21]  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).

[22]  K. Gu,et al.  Discretized Lyapunov functional for linear uncertain systems with time-varying delay , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[23]  Silviu-Iulian Niculescu,et al.  Additional dynamics in transformed time-delay systems , 2000, IEEE Trans. Autom. Control..

[24]  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).