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CLC number: O231.4

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Received: 2004-02-02

Revision Accepted: 2004-07-28

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.4 P.311~314

http://doi.org/10.1631/jzus.2005.A0311


Differentiability of the Pritchard-Salamon systems with admissible state-feedback


Author(s):  YU Xin

Affiliation(s):  Laboratory of Information and Optimization Technology, Ningbo Institute of Technology, Zhejiang University, Ningbo 315104, China

Corresponding email(s):   yuxin@zju.edu.cn

Key Words:  C0-semigroup, Differentiability, Admissible operator, Pritchard-Salamon systems, Perturbation


YU Xin. Differentiability of the Pritchard-Salamon systems with admissible state-feedback[J]. Journal of Zhejiang University Science A, 2005, 6(4): 311~314.

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journal="Journal of Zhejiang University Science A",
volume="6",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0311"
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T1 - Differentiability of the Pritchard-Salamon systems with admissible state-feedback
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A0311


Abstract: 
Due to the fact that many papers on a wide range of control problems for pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed, this paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Curtain, R.F., 1996. The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. Systems & Control Letters, 27:67-72.

[2] Curtain, R.F., Zwart, H., 1994. The Nehari problem for the Pritchard-Salamon class of infinite-dimensional linear systems: A direct approach. Integr Equ Oper Theory, 18:130-153.

[3] Curtain, R.F., Zwart, H., 1995. An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, New York.

[4] Curtain, R.F., Weiss, M., Zhou Y., 1996. Closed formulae for a parametric-mixed-sensitivity problem for Pritchard-Salamon systems. Systems & Control Letters, 27:157-167.

[5] Curtain, R.F., Logemann, H., Townley, S., Zwart, H., 1997. Well-posedness, stabilizability and admissibility for Pritchard-Salamon systems. J Math Systems Estimation, Control, 7:439-476.

[6] Gu, X.H., 2004. Robustness with respect to Variable Small Delays for Exponential Stability of Infinite-dimensional Linear Systems and Unbounded Perturbation. PH.D Dissertation, Sichuan University, Chengdu (in Chinese).

[7] Guo, F.M., Zhang, Q., Huang, F.L., 2003. On well-posedness and admissible stabilizability for Pritchard-Salamon systems. Applied Math. Letters, 16:65-70.

[8] Pazy, A., 1968. On the differentiability and compactness of semigroups of linear operators. J Math Mech, 17:1131-1141.

[9] Pazy, A., 1983. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag.

[10] Pritchard, A.J., Salamon, D., 1985. The linear quadratic control problem for retarded systems with delays in control and observation. IMA J Math Control & Information, 2:335-362.

[11] Pritchard, A.J., Salamon, D., 1987. The linear quadratic control problem for infinite-dimensional systems with unbounded input and output operators. SIAM J Control Optim, 25:121-144.

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