Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Controllability of a class of linear systems in Banach space


Author: Quan Zheng
Journal: Proc. Amer. Math. Soc. 123 (1995), 1241-1251
MSC: Primary 93B05; Secondary 34G10, 34H05, 47N70
DOI: https://doi.org/10.1090/S0002-9939-1995-1203996-1
MathSciNet review: 1203996
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies the notions of controllability for the linear systems associated with the generator of an exponentially bounded C-semigroup in a Banach space, controls also belonging to Banach spaces. Necessary and sufficient conditions are obtained in that framework, and the duality property is studied, which generalize the corresponding results of the linear systems associated with the generator of a strongly continuous semigroup.


References [Enhancements On Off] (What's this?)

  • [1] R. F. Curtain and A. J. Pritchard, Infinite dimensional linear systems theory, Springer-Verlag, Berlin, 1978. MR 516812 (80h:93002)
  • [2] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248. MR 0225199 (37:793)
  • [3] E. B. Davies and M. M. H. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. (3) 55 (1987), 181-208. MR 887288 (88e:34100)
  • [4] R. deLaubenfels, C-existence families and improperly posed problems, Semesterbericht Funktionalanlysis, vol. 17, Tübingen, Wintersemester, 1989/90, pp. 155-170.
  • [5] S. Dolecki and D. L. Russell, A general theory of observation and control, SIAM J. Control Optim. 15 (1977), 185-220. MR 0451141 (56:9428)
  • [6] I. Miyadera and N. Tanaka, A remark on exponentially bounded C-semigroups, Proc. Japan Acad. Ser. A 66 (1990), 31-34. MR 1051847 (91i:47054)
  • [7] D. L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Review 20 (1978), 639-739. MR 508380 (80c:93032)
  • [8] N. Tanaka, On perturbation theory for exponentially bounded C-semigroups, Semigroup Forum 41 (1990), 215-236. MR 1057592 (91c:47079)
  • [9] N. Tanaka and I. Miyadera, Exponentially bounded C-semigroups and integrated semigroups, Tokyo J. Math. 12 (1989), 99-115. MR 1001735 (90g:47081)
  • [10] K. N. Wang, Controllability and observability for distributed parameter control systems, Acta Math. Sci. 2 (1982), 403-420. (Chinese) MR 737068 (85e:93026)
  • [11] K. Yosida, Functional analysis, Springer-Verlag, Berlin, 1966.
  • [12] Q. Zheng, Global solutions of abstract differential equations and applications, Acta Math. Sci. 11 (1991), 225-233. (Chinese) MR 1129757 (92h:34111)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 93B05, 34G10, 34H05, 47N70

Retrieve articles in all journals with MSC: 93B05, 34G10, 34H05, 47N70


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1203996-1
Keywords: Controllability, complete controllability, C-semigroup
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society