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| Stability of a Class of Linear Systems on Hilbert Space | |
| 引用本文： | 谢灵红,谢建华. Stability of a Class of Linear Systems on Hilbert Space[J]. 西南交通大学学报(英文版), 2005, 13(1): 84-86 |
| 作者姓名： | 谢灵红 谢建华 |
| 作者单位： | Department of Applied Mathematics，Southwest Jiaotong University，Chengdu 610031，China，Department of Applied Mechanics and Engineering，Southwest Jiaotong University，Chengdu 610031，China |
| 基金项目： | TheNationalNatureScienceFoundationofChina(No.10472096). |
| 摘 要： | Thelinearcontrolsystemunderstudyisddtx(t)=Ax(t) Bu(t), t>0x(0)=x0,(1)whereAisthegeneratorofanexponentiallystableC semigroupT(t)inaHilbertspaceX, andBisaboundedoperatorfromtheHilbertspaceYtoX.Eq. (1) hasreceivedmuchattentionunderthehy pothesisthatAgenerate… |
| 关 键 词： | 稳定性 线性控制系统 希尔伯特空间 C半群 |
Stability of a Class of Linear Systems on Hilbert Space |
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| Xie Linghong,Xie Jianhua. Stability of a Class of Linear Systems on Hilbert Space[J]. Journal of Southwest Jiaotong University, 2005, 13(1): 84-86 | |
| Authors: | Xie Linghong Xie Jianhua |
| Abstract: | Consider the linear control systems x′(t)=Ax(t)+Bu(t)(t＞0), x(0)=x0 , where A is the generator of an exponentially stable C-semigroup on a Hilbert space X, B is a bounded operator from the Hilbert space Y to X. In the condition that the resolvent set A is not empty and the range of C is dense in X, we obtain that the extended controllability map is the unique self-adjoint solution to the Lyapunov equation. Moreover, sufficient conditions for asymptotically stability of C-semigroup are given. |
| Keywords: | C-semigroup Linear control system Asymptotic stability Lyapunov equation |
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