Passive linear time-varying systems: State-space realizations, stability in feedback, and controller synthesis
Passive linear time-varying systems: State-space realizations, stability in feedback, and controller synthesis
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DOI：
10.1109/acc.2010.5530792
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发表时间：
2010-07
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影响因子：
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通讯作者：
J. Forbes;C. Damaren
中科院分区：
文献类型：
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作者：
J. Forbes;C. Damaren
本文研究线性时变无源系统。我们陈述了各种定理，这些定理依赖于系统的状态空间矩阵，这些定理可以识别线性时变系统何时是纯被动的，输入严格被动的，输出严格被动的，或输入-状态严格被动的，这是本文中定义的被动性的非标准概念。我们的两个定理类似于卡尔曼-雅库博维奇-波波夫引理，一个适用于时变系统的馈通矩阵和线性时变系统没有一个。考虑了各种系统的负反馈互联。证明了一个输出严格无源系统与一个输入状态严格无源系统负关联时是全局渐近稳定的。我们还表明，线性时变输入状态和输出严格无源系统连接在负反馈与一个部门有界，无记忆非线性也是全局渐近稳定的。时变输出严格无源控制器的最优设计也被考虑。我们给出一个例子：时变质量的位置和速度控制通过动态时变补偿器和扇区有界的无记忆非线性控制。
In this paper we consider linear time-varying passive systems. We state various theorems, which rely on the state-space matrices of the system, that identify when a linear-time varying system is purely passive, input strictly passive, output strictly passive, or input-state strictly passive which is a nonstandard notion of passivity defined in this paper. Two of our theorems resemble the Kalman-Yakubovich- Popov Lemma, one applicable to time-varying systems with a feedthrough matrix and the other for linear time-varying systems without one. The negative feedback interconnection of various systems is considered. We show that an output strictly passive system negatively interconnected with an input-state strictly passive system is globally asymptotically stable. We also show that both linear time-varying input-state and output strictly passive systems when connected in negative feedback with a sector bounded, memoryless nonlinearity are also globally asymptotically stable. The optimal design of a time-varying output strictly passive controller is also considered. We present an example: the position and velocity control of a time-varying mass controlled via a dynamic time-varying compensator and a sector bounded, memoryless nonlinearity.