Global stabilization of oscillators with bounded delayed input

The problem of globally asymptotically stabilizing by bounded feedback of an oscillator with an arbitrary large delay in the input is solved. A first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term. Next, it is shown through a Lyapunov analysis that the stabilization can be achieved as well when neglecting the distributed terms. It turns out that this main result is intimately related to the output feedback stabilization problem.

[1]  Sabine Mondié,et al.  Global asymptotic stabilization for chains of integrators with a delay in the input , 2003, IEEE Trans. Autom. Control..

[2]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[3]  William S. Levine,et al.  The Control Handbook , 2005 .

[4]  O Smith,et al.  CLOSER CONTROL OF LOOPS WITH DEAD TIME , 1957 .

[5]  Masami Ito,et al.  A process-model control for linear systems with delay , 1981 .

[6]  Z. Artstein.  Linear systems with delayed controls: A reduction , 1982 .

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

[8]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[9]  Chaouki T. Abdallah,et al.  Delay effects on static output feedback stabilization , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  I. Mufti.  A note on the stability of an equation of third order with time lag , 1964 .

[11]  Sabine Mondié,et al.  Approximation of control laws with distributed delays: a necessary condition for stability , 2001, Kybernetika.

[12]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[13]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

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

[15]  R. Lozano,et al.  Resetting process-model control for unstable systems with delay , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[17]  H. I. Ansoff,et al.  A general stabilty criterion for linear oscillating systems with constant time lag , 1948 .

[18]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .