Weighted sensitivity minimization in systems with a single input delay: A state space solution

SIAM Journal on Control and Optimization

Volumn 35, Issue 5, 1997, Pages 1445-1469

  Tadmor, Gilead ^a  

^a Northeastern University   (United States)

Author keywords

Input delay; Matrix Riccati equations; Nehari problem; State space solutions

Indexed keywords

MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; RICCATI EQUATIONS; SENSITIVITY ANALYSIS; STATE SPACE METHODS;

INPUT DELIVERY; NEHARI PROBLEMS;

CONTROL SYSTEM ANALYSIS;

EID: 0031232878     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995279651     Document Type: Article

References (36)

1. p corresponding to differential equations with delays, Canad. J. Math., 30 (1977), pp. 897-914.
2. J. A. BURNS, T. L. HERDMAN, AND H. W. STECH, The Cauchy problem for linear functional differential equations, in Integral and Differential Equations, T. L. Herdman, S. M. Rankin, and H. W. Stech, eds., Marcel Dekker, New York, 1981, pp. 139-149.
3. J. A. BURNS, T. L. HERDMAN, AND H. W. STETCH, Linear functional differential equations as semigroups on product spaces, SIAM J. Math. Anal., 14 (1983), pp. 98-116.
4. R. F. CURTAIN AND A. J. PRITCHARD, Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, 1978.
5. R. F. CURTAIN AND H. J. ZWART, An Introduction to Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.
6. M. C. DELFOUR, The largest class of hereditary systems defining a co-semigroup on the product space, Canad. J. Math., 32 (1980), pp. 969-978.
7. ∞ sensitivity minimization for delay systems, System Control Lett., 9 (1987), pp. 17-24.
8. C. FOIAS, A. TANNENBAUM, AND G. ZAMES, Weighted sensitivity minimization for delay systems, IEEE Trans. Automat. Control, AC 31 (1986), pp. 763-766.
9. ∞ Control Theory, Springer-Verlag, Berlin, 1986.
10. E. HILLE AND R. S. PHILLIPS, Functional Analysis and Semigroups, AMS Colloquium Publications XXXI, Providence, RI, 1957.
11. A. ICHIKAWA, Optimal Control and Filtering of Evolution Equations with Delays in Control and Observation, Tech. Rep. 53, Control Theory Centre, University of Warwick, UK, 1977.
12. M. A. KAASHOEK AND J. KOS, The Nehari-Takagi problem for input-output operators of time varying continuous time systems, Integral Equations Operator Theory, 18 (1994), pp. 435-467.
13. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1972.
14. ∞ control with transients, SIAM J. Control Optim., 29 (1991), pp. 1373-1393.
15. ∞ Control and estimations problems with delayed measurements: State space solutions, in Proceedings of the American Control Conference, 1994, pp. 2379-2383.
16. Z. NEHARI, On bounded bilinear forms, Ann. of Math., 65 (1957), pp. 153-162.
17. ∞ optimal control of multivariable distributed systems, SIAM J. Control Optim., 28 (1990), pp. 653-670.
18. A. PAZY, Semigroups of Linear Operators and Relations to Differential Equations, Springer-Verlag, New York, 1983.
19. A. J. PRITCHARD AND D. SALAMON, The linear-quadratic problem for retarded systems with delays in the control and observation, IMA J. Math. Control Inform., (1985), pp. 335-362.
20. A. J. PRITCHARD AND D. SALAMON, The linear-quadratic problem for infinite dimensional systems with unbounded input and output operators, SIAM J. Control Optim., 25 (1987), pp. 121-144.
21. D. SALAMON, Control and Observation of Neutral Systems, Pitman, Boston, 1984.
22. ∞, Trans. Amer. Math. Soc., 127 (1967), pp. 179-203.
23. B. SZ.-NAGY AND C. FOIAŞ, Harmonic Analysis of Operators on Hilbert Spaces, North Holland, Amsterdam, 1970.
24. ∞ optimization in systems with distributed lags, System Control Lett., 8 (1987), pp. 313-319.
25. ∞ interpolation in systems with commensurate input lags, SIAM J. Control Optim., 27 (1989), pp. 511-526.
26. G. TADMOR, I/O norms in general linear systems, Internat. J. Control, 51 (1990), pp. 911-921.
27. ∞ problem, Math. Control Signals Systems, 3 (1990), pp. 301-324.
28. ∞ problem and the maximum principle: The general linear case, SIAM J. Control Optim., 31 (1993), pp. 831-846.
29. ∞ control in systems with a single input lag, in Proceedings of the American Control Conference, 1995, pp. 321-325.
30. G. TADMOR, Robust control in the gap: A state space solution in the presence of a single input delay, IEEE Trans. Automat. Control, in press.
31. G. TADMOR AND J. TURI, Neutral equations and associated semigroups, J. Differential Equations, 116 (1995), pp. 59-87.
32. G. TADMOR AND M. VERMA, Factorization and the Nehari theorem in time varying systems, Math. Control Signals Systems, 5 (1992), pp. 419-452.
33. ∞ Control for Infinite Dimensional Systems: A State Space Approach, Ph.D. thesis, University of Groningen, Groningen, The Netherlands, 1993.
34. 2: Properties of the generator, J. Inst. Math. Appl., 21 (1978), pp. 13-23.
35. R. B. VINTER AND R. H. KWONG, The infinite time quadratic control problem for linear systems with state and control delays: An evolution approach, SIAM J. Control Optim., 19 (1981), pp. 139-153.
36. K. ZHOU AND P. P. KHARGONEKAR, On the weighted sensitivity minimization problem for delay systems, System Control Lett., 8 (1987), pp. 307-312.