| Stability of a Class of Linear Systems on Hilbert Space |
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| 作者姓名： | 谢灵红 谢建华 |
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| 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 |
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| 基金项目： | TheNationalNatureScienceFoundationofChina(No.10472096). |
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| 摘 要： | Thelinearcontrolsystemunderstudyisddtx(t)=Ax(t) Bu(t), t>0x(0)=x0,(1)whereAisthegeneratorofanexponentiallystableC semigroupT(t)inaHilbertspaceX, andBisaboundedoperatorfromtheHilbertspaceYtoX.Eq. (1) hasreceivedmuchattentionunderthehy pothesisthatAgenerate…
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| 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. |
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| Authors: | Xie Linghong Xie Jianhua |
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| 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. |
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| Keywords: | C-semigroup Linear control system Asymptotic stability Lyapunov equation |
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