Coprime factorizations and well-posed linear systems

SIAM Journal on Control and Optimization

Volumn 36, Issue 4, 1998, Pages 1268-1292

  Staffans, Olof J ^a  

^a ÅBO AKADEMI UNIVERSITY   (Finland)

Author keywords

Detectability; Input output stability; Stabilizability

Indexed keywords

CONTROL SYSTEM ANALYSIS; OPTIMAL CONTROL SYSTEMS; SYSTEM STABILITY; TRANSFER FUNCTIONS;

COPRIME FACTORIZATION;

LINEAR CONTROL SYSTEMS;

EID: 0032123919     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995285417     Document Type: Article

References (33)

1. R. F. CURTAIN, Representations of infinite-dimensional systems, in Three Decades of Mathematics Systems Theory. A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems, Lecture Notes in Control and Information Sciences 135, H. Nijmeijer and J. M. Schumacher, eds., Springer-Verlag, Berlin, New York, 1989, pp. 101-128.
2. R. F. CURTAIN, A synthesis of time and frequency domain methods for the control of infinite-dimensional systems: A system theoretic approach, in Control and Estimation in Distributed Parameter Systems, Frontiers in Applied Mathematics, H. T. Banks, ed., SIAM, Philadelphia, PA, 1992, pp. 171-224.
3. R. F. CURTAIN AND G. WEISS, Well posedness of triplets of operators (in the sense of linear systems theory), in Control and Optimization of Distributed Parameter Systems, Birkhäuser-Verlag, Basel, 1989, pp. 401-416.
4. R. F. CURTAIN AND G. WEISS, Dynamic stabilization of regular linear systems, IEEE Trans. Automat. Control, 42 (1996), pp. 1-18.
5. R. F. CURTAIN, G. WEISS, AND M. WEISS, Coprime factorization for regular linear systems, Automatica, 32 (1996), pp. 1519-1531.
6. R. F. CURTAIN, G. WEISS, AND M. WEISS, Stabilization of irrational transfer functions by controllers with internal loop, Automatica, 1997, submitted.
7. F. FLANDOLI, I. LASIECKA, AND R. TRIGGIANI, Algebraic (Riccati) equations with non-smoothing observation arising in hyperbolic and (Euler-Bernuolli) boundary control problems, Ann. Mat. Pura Appl., 153 (1988), pp. 307-382.
8. Y. FOURÈS AND I. E. SEGAL, Causality and analyticity, Trans. Amer. Math. Soc., 78 (1955), pp. 385-405.
9. 2[0, ∞), Math. Control Signals Systems, 6 (1993), pp. 195-223.
10. S. HANSEN AND G. WEISS, New results on the operator Carleson measure criterion, IMA J. Math. Control Inform., 14 (1997), pp. 3-32.
11. B. JACOB AND H. ZWART, Equivalent Conditions for Stabilizability of Infinite-dimensional Systems with Admissible Control Operators, preprint, 1996.
12. H. LOGEMANN, Stabilization and regulation of infinite-dimensional systems using coprime factorizations, in Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems, Lecture Notes in Control and Information Sciences 185, Springer-Verlag, Berlin, New York, 1993, pp. 102-139.
13. K. A. MORRIS, State feedback and estimation of well-posed systems, Math. Control Signals Systems, 7 (1994), pp. 351-388.
14. R. OBER AND S. MONTGOMERY-SMITH, Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions, SIAM J. Control Optim., 28 (1990), pp. 438-465.
15. A. J. PRITCHARD AND D. SALAMON, The linear-quadratic control problem for retarded systems with delays in control and observation, IMA J. Math. Control Inform., 2 (1985), pp. 335-362.
16. A. J. PRITCHARD AND D. SALAMON, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators, SIAM J. Control Optim., 25 (1987), pp. 121-144.
17. R. REBARBER, Conditions for the equivalence of internal and external stability for distributed parameter systems, IEEE Trans. Automat. Control, 38 (1993), pp. 994-998.
18. D. SALAMON, Control and Observation of Neutral Systems, Pitman Publishing Ltd., London, 1984.
19. D. SALAMON, Infinite dimensional linear systems with unbounded control and observation: A functional analytic approach, Trans. Amer. Math. Soc., 300 (1987), pp. 383-431.
20. D. SALAMON, Realization theory in (Hilbert) space, Math. Systems Theory, 21 (1989), pp. 147-164.
21. M. C. SMITH, On stabilization and the existence of coprime factorizations, IEEE Trans. Automat. Control, 34 (1989), pp. 1005-1007.
22. O. J. STAFFANS, Quadratic optimal control of stable systems through spectral factorization, Math. Control Signals Systems, 8 (1995), pp. 167-197.
23. O. J. STAFFANS, Quadratic Optimal Control Through Coprime and Spectral Factorizations, Technical Reports on Computer Science & Mathematics, Series A 178, Åbo Akademi University, Åbo, Finland, 1996.
24. O. J. STAFFANS, Quadratic optimal control of stable well-posed linear systems, Trans. Amer. Math. Soc., 349 (1997), pp. 3679-3715. 1997, to appear.
25. O. J. STAFFANS, Quadratic optimal control of well-posed linear systems, SIAM J. Control Optim., to appear.
26. ∞-Control for Distributed Parameter Systems: A State Space Approach, Birkhäuser-Verlag, Basel, Boston, Berlin, 1993.
27. G. WEISS, Admissibility of unbounded control operators, SIAM J. Control Optim., 27 (1989), pp. 527-545.
28. G. WEISS, Admissible observation operators for linear semigroups, Israel J. Math., 65 (1989), pp. 17-43.
29. ∞, Math. Control Signals Systems, 4 (1991), pp. 193-203.
30. G. WEISS, Transfer functions of regular linear systems. Part I: Characterizations of regularity, Trans. Amer. Math. Soc., 342 (1994), pp. 827-854.
31. G. WEISS, Regular linear systems with feedback, Math. Control Signals Systems, 7 (1994), pp. 23-57.
32. G. WEISS AND H. ZWART, An example in linear quadratic optimal control, Systems Control Lett., 1998.
33. M. WEISS AND G. WEISS, Optimal control of stable weakly regular linear systems, Math. Control Signals Systems, 1997.