Stability of periodically time-varying systems: Periodic Lyapunov functions
Stability of periodically time-varying systems: Periodic Lyapunov functions
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DOI：
10.1016/j.automatica.2012.06.070
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
C. Böhm;M. Lazar;F. Allgöwer
中科院分区：
文献类型：
--
作者：
C. Böhm;M. Lazar;F. Allgöwer
提出了一种新的离散非线性周期时变系统稳定性分析方法。捐款情况如下。首先，放松标准李雅普诺夫条件。这导致一个保守性较低的李雅普诺夫函数，需要减少在每个周期，而不是在每个时刻。其次，对于线性周期系统的约束，它表明，相比标准的李雅普诺夫理论，新的概念，周期李雅普诺夫函数允许计算一个更大的估计的吸引区域。算例表明了该理论的有效性。
This paper proposes a novel approach to stability analysis of discrete-time nonlinear periodically time-varying systems. The contributions are as follows. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at each period rather than at each time instant. Secondly, for linear periodic systems with constraints, it is shown that compared to standard Lyapunov theory, the novel concept of periodic Lyapunov functions allows for the calculation of a larger estimate of the region of attraction. An example illustrates the effectiveness of the developed theory.