Necessary condition of linear distributed parameter systems with exact controllability

被引：2
|
作者：
Xu, Gen Qi [1 ]
机构：
[1] Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China
来源：
SYSTEMS & CONTROL LETTERS | 2018年 / 118卷
关键词：
Linear system; Exact controllability; Necessary condition; Immediately norm-continuous semigroup; EXACT OBSERVABILITY; HILBERT-SPACES; BANACH-SPACES; APPROXIMATE CONTROLLABILITY; DIFFERENTIAL-EQUATIONS; MILD SOLUTIONS; PERTURBATIONS; ROBUSTNESS; STABILIZABILITY; GENERATOR;
D O I：
10.1016/j.sysconle.2018.06.004
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we studied the necessary condition of distributed parameter system with exact controllability. Let Phi(t)(0) be the control mapping. We introduce new a class of control operators that is called the I-class control which satisfy R(Phi(t)(0)) boolean AND R(T(t)) is closed set for t > 0. If the system is exactly controllable in finite time tau, then the semigroup T(t) must have closed range. In particular, if the generator of T(t) has compact resolvent, its spectra distribute in a strip parallel to imaginary axis. As an application we assert that the systems associated with the immediately norm-continuous semigroups are never exact controllable for zero-class or I-class controls. (C) 2018 Elsevier B.V. All rights reserved.
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页码：109 / 115
页数：7
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