From PDEs with boundary control to the abstract state equation with an unbounded input operator: A tutorial

European Journal of Control

Volumn 6, Issue 1, 2000, Pages 27-49

  Emirsjlow, Zbigniew ^a   Townley, Stuart ^b  

^a WEST POMERANIAN UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Boundary control systems; Infinite dimensional systems with unbounded input operators; Operator differential equations; Partial differential equations with non homogeneous boundary conditions

Indexed keywords

EID: 28444468568     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0947-3580(00)70908-3     Document Type: Article

References (21)

1. Adams R. Sobolev spaces. Academic Press, New York 1976
2. Aubin JP. Applied functional analysis. John Wiley and Sons, New York 1979
3. Bensoussan A, Da Prato G, Delfour MC, Mitter SK. Representation and control of infinite dimensional systems, vol. I. Birkhäuser, Boston 1992
4. Curtain RF, Pritchard AJ. Infinite-dimensional systems theory. Springer-Verlag, Berlin, 1978
5. Curtain RF, Zwart H. An introduction to infinite-dimensional linear systems theory, Springer-Verlag, New York 1995
6. Emirsjlow Z, Pritchard AJ, Townley S. On structured perturbation for two classes of linear infinite-dimensional systems. Dynamics and control 1996; 6(2): 227-261
7. Fattorini HO. Boundary control systems. SIAM J control 1968; 6(3): 349-385
8. Fattorini HO. The Cauchy problem. Addison-Wesley Company, Reading (USA) 1983
9. Fattorini HO. Second order linear differential equations in banach spaces. Elsevier Science Publishers, Amsterdam 1985
10. Flandoli F, Lasiecka I, Triggiani R. Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems. Annali di Matematica pura ed applicata 1998; CLIII: 307-382
11. Lasiecka I. Unified theory for abstract parabolic boundary problems - a semigroup approach. Applied mathematics & optimization 1980; 6: 287-333
12. 2(Γ)-boundary input hyperbolic equations. Applied mathematics and optimization 1981; 7: 35-93
13. Lasiecka I, Triggiani R. Differential and algebraic Riccati equations with applications to boundary/point control problems: Continuous theory and approximation theory. LNCIS No. 164, Springer-Verlag, Berlin 1991
14. Lions JL. Optimal control of systems governed by partial differential equations. Springer-Verlag, Berlin 1971
15. Pazy A. Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York 1983
16. Pritchard AJ, Salamon D. The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators. SIAM J Control Optimization 1987; 25: 121-144
17. Salamon D. Infinite dimensional linear systems with unbounded control and observation: A functional analytic approach. Transactions AMS 1987; 30: 383-431
18. 2. Systems and Control Letters 1988; 10: 79-82
19. Weiss G. Admissible observation operators for linear semigroups. Israeli J Mathematics 1989; 65(1): 17-43
20. Weiss G. Admissibility of unbounded control operators. SIAM J Control Optimization 1989; 27(3): 527-545
21. Weiss G. The representation of regular linear systems on Hilbert spaces. In: Control and estimation of distributed parameter systems, Kappel F, Klinisch K, Schappacher W (eds). Birkhäuser, Basel 1989, pp. 401-416