Exact controllability of C0-groups with one-dimensional input operators

被引:0
|
作者
Jacob, B [1 ]
Zwart, H [1 ]
机构
[1] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England
来源
ADVANCES IN MATHEMATICAL SYSTEMS THEORY: A VOLUME IN HONOR OF DIEDERICH HINRICHSEN | 2001年
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中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Assume that A generates a C-0-group T(t) on the complex, separable Hilbert space H, and that b epsilon D(A*)' is an admissible control operator for the semigroup T(t). It is known that exact controllability of the system defined by A and b implies that every element of the spectrum of A is an eigenvalue. We develop equivalent conditions for exact controllability of the system defined by A and b. These conditions are given in terms of the eigenvalues and eigenvectors of A and the control operator b. Also necessary conditions are included. A necessary condition is that one over the eigenvalues is a sequence in l(1+epsilon), epsilon > 0. If additionally, A is a diagonal operator, then we prove that the conjecture of Russell and Weiss [12] holds.
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页码:221 / 242
页数:22
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