Robustness with respect to delays for exponential stability of distributed parameter systems

SIAM Journal on Control and Optimization

Volumn 37, Issue 1, 1999, Pages 230-244

  Rebarber, Richard ^a   Townley, Stuart ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Control; Delays; Distributed parameter systems; Feedback; Robustness

Indexed keywords

CONTROL SYSTEM ANALYSIS; FEEDBACK CONTROL; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

EXPONENTIAL STABILITY;

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 0032155657     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012996312453     Document Type: Article

References (24)

1. R.F. CURTAIN, Equivalence of input-output stability and exponential stability for infinite dimensional systems, Math. Systems Theory, 21 (1988), pp. 19-48.
2. R. CURTAIN AND H. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts Appl. Math. 21, Springer-Verlag, New York, 1995.
3. R. DATKO, J. LAGNESE, AND M.P. POLIS, An example of the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim., 24 (1986), pp. 152-156.
4. R. DATKO, Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks, SIAM J. Control Optim., 26 (1988), pp. 697-713.
5. R. DATKO AND Y.C. YOU, Some second-order vibrating systems cannot tolerate small delays in their damping, J. Optim. Theory Appl., 70 (1991), pp. 521-537.
6. P. GRISVARD, Equations differentielles abstraites, Ann. Sci. École Norm. Sup., 2 (1969), pp. 311-395.
7. 2, Systems Control Lett., 16 (1991), pp. 219-227.
8. C.A. JACOBSON AND C.N. NETT, Linear state-space systems in infinite-dimensional space: The role and characterization of joint stabilizability/detectability, IEEE Trans. Automat. Control, 38 (1993) pp. 994-998.
9. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, New York, 1980.
10. H. LOGEMANN, R. REBARBER, AND G. WEISS, Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop, SIAM J. Control Optim., 34 (1996), pp. 572-600.
11. H. LOGEMANN AND R. REBARBER, The effect of small time-delays on the closed-loop stability of boundary control systems, Math. Control Signals Systems, 9 (1996), PP. 123-151.
12. H. LOGEMANN AND S. TOWNLEY, The effect of small delays in the feedback loop on the stability of neutral systems, Systems Control Lett., 27 (1996), pp. 267-274.
13. J. PRÜSS, On the spectrum of Co-semigroups, Trans. Amer. Math. Soc., 24 (1984), pp. 847-857.
14. R. REBARBER, Necessary conditions for exponential stabilizability of distributed parameter systems with infinite dimensional unbounded feedback, Systems Control Lett., 14 (1990), pp. 241-248.
15. R. REBARBER, Conditions for the equivalence of internal and external stability for distributed parameter systems, IEEE Trans. Automat. Control, 38 (1993), pp. 994-998.
16. R. REBARBER AND H. ZWART, Open loop stabilizability of infinite dimensional systems, Math. Control Signals Systems, to appear.
17. D. SALAMON, Control and Observation of Neutral Systems, Res. Notes Math. 91, Pitman, Boston, MA, 1984.
18. R. TRIGGIANI, On the stabilizability problem in Banach space, J. Math. Anal. Appl., 52 (1975), pp. 383-403.
19. R. TRIGGIANI, Wave equation on a bounded domain with boundary dissipation: An operator approach, J. Math. Anal. Appl., 137 (1989), pp. 438-461.
20. G. WEISS, Admissibility of unbounded control operators, SIAM J. Control Optim., 27 (1989), pp. 527-545.
21. G. WEISS, Two conjectures on the admissibility of control operators, in Estimation and Control of Distributed Parameter Systems, W. Desch, F. Kappel, and K. Kunisch, eds., Birkhäuser-Verlag, Basel, 1991, pp. 367-378.
22. G. WEISS, Transfer functions of regular linear systems, part I: Characterization of regularity, Trans. Amer. Math. Soc., 342 (1994), pp. 827-854.
23. G. WEISS, Regular linear systems with feedback, Math. Control Signals Systems, 7 (1994), pp. 23-57.
24. H.J. ZWART, Some remarks on open and closed loop stabilizability for infinite dimensional systems, in Control and Estimation of Distributed Parameter Systems, Internat. Ser. Numer. Math. 91, F. Kappel, K. Kunisch, and W. Schappacher, eds., Birkhäuser-Verlag, Basel, 1989, pp. 425-434.