Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations
Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations
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混合无源性和有限增益稳定性定理：具有无源性违规的系统的稳定性和控制
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
C. Damaren
中科院分区：
文献类型：
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作者：
J. Forbes;C. Damaren
研究了具有无源性违逆的系统的稳定性和控制问题。作者试图利用有限增益特性的植物在一个范围内，其中一个被动映射不再存在，而实现类似的混合被动和有限增益控制器。利用耗散系统框架，定义了一种混合系统，即具有被动映射和被动映射被破坏时有限增益特性的混合系统。混合系统的定义利用一个开关参数将系统分成无源和有限增益区域。结果表明，该开关参数等效于理想低通滤波器，可以用巴特沃斯滤波器逼近。本文还考虑了两个混合系统在负反馈互连中的稳定性问题。利用李雅普诺夫技术和输入输出技术建立了一个混合无源性和有限增益稳定性定理，得到了等效的结果。给出了闭环系统稳定的充分条件，它类似于传统无源定理和小增益定理的结合。
The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal low-pass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input-output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.