Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion
Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion
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DOI：
10.1109/tac.2008.929368
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发表时间：
2008-09
影响因子：
6.8
通讯作者：
Weihai Zhang;Huanshui Zhang;Bor‐Sen Chen
中科院分区：
文献类型：
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作者：
Weihai Zhang;Huanshui Zhang;Bor‐Sen Chen
本文利用广义Lyapunov方程方法研究了带状态乘性噪声的随机镇定/可检测性问题。得到了随机镇定和可检测性的一些实用判据，如精确可检测性的随机Popov-Belevitch-Hautus判据。此外，基于文中介绍的临界稳定性和精确可检测性，得到了广义Lyapunov方程的有用性质。作为应用，首先对随机线性二次型调节器以及相关的广义代数Riccati方程进行了广泛的讨论。其次，研究了具有状态和控制相关噪声的无限水平随机H2/H inin控制问题，推广和改进了最近发表的结果。
In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and detectability, such as stochastic Popov-Belevitch-Hautus criterion for exact detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic H 2/H infin control with state- and control-dependent noise is also investigated, which extends and improves the recently published results.