Sufficient conditions for function space controllability and feedback stabilizability of linear reta
Sufficient conditions for function space controllability and feedback stabilizability of linear reta
复制标题
线性回归函数空间可控性和反馈稳定性的充分条件
DOI：
10.1109/cdc.1976.267670
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
R. Triggiani
中科院分区：
文献类型：
--
作者：
A. Manitius;R. Triggiani
New sufficient conditions for function space controllability and hence feedback stabilizability of linear retarded systems are presented. These conditions were obtained by treating the retarded systems as a special case of an abstract equation in Hilbert space R^{n}\times L_{2}([- h, 0], R^{n}) (denoted as M_{2 }). For systems of type \cdot{x}(t)=A_{0}x(t)+A_{1}x(t-h)+Bu(t) , it is shown that most of controllability properties are described by a certain polynomial matrix P(\lambda) , whose columns can be generated by an algorithm comparing A_{0}^{i}B,A_{0}^{i} B and mixed powers of A 0 and A 1 multiplied by B. It is shown that the M 2 -approximate controllability of the system is guaranteed by certain triangularity properties of P(\lambda) . By using the Luenberger canonical form, it is shown that the system is M 2 -approximately controllable if the pair (A_{1},B) is controllable and if each of the spaces spanned by columns of [B,A_{1}B,... ,A_{1}^{j}B], j=O...n-1 , is invariant under transformation A 0 . Other conditions of this type are also given. Since the M 2 -approximate controllability implies controllability of all the eigenmodes of the system, the feedback stabilizability with an arbitrary exponential decay rate is guaranteed under hypotheses leading to M 2 -approximate controllability. Some examples are given.
New sufficient conditions for function space controllability and hence feedback stabilizability of linear retarded systems are presented. These conditions were obtained by treating the retarded systems as a special case of an abstract equation in Hilbert space R^{n}\times L_{2}([- h, 0], R^{n}) (denoted as M_{2 }). For systems of type \cdot{x}(t)=A_{0}x(t)+A_{1}x(t-h)+Bu(t) , it is shown that most of controllability properties are described by a certain polynomial matrix P(\lambda) , whose columns can be generated by an algorithm comparing A_{0}^{i}B,A_{0}^{i} B and mixed powers of A 0 and A 1 multiplied by B. It is shown that the M 2 -approximate controllability of the system is guaranteed by certain triangularity properties of P(\lambda) . By using the Luenberger canonical form, it is shown that the system is M 2 -approximately controllable if the pair (A_{1},B) is controllable and if each of the spaces spanned by columns of [B,A_{1}B,... ,A_{1}^{j}B], j=O...n-1 , is invariant under transformation A 0 . Other conditions of this type are also given. Since the M 2 -approximate controllability implies controllability of all the eigenmodes of the system, the feedback stabilizability with an arbitrary exponential decay rate is guaranteed under hypotheses leading to M 2 -approximate controllability. Some examples are given.