Trace formula of linear continuous-time periodic systems via the harmonic Lyapunov equation
Trace formula of linear continuous-time periodic systems via the harmonic Lyapunov equation
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DOI：
10.1080/0020717031000091441
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发表时间：
2003-01
影响因子：
2.1
通讯作者：
Jun Zhou-;T. Hagiwara;M. Araki
中科院分区：
文献类型：
--
作者：
Jun Zhou-;T. Hagiwara;M. Araki
在本文的前半部分，基于调和李雅普诺夫方程的解，建立了一类有限维线性连续时间周期（FDLCP）系统的H2模的迹公式。这个迹公式在形式上与我们对LTI连续时间系统的H 2范数的形式非常相似，除了在FDLCP设置中涉及无限维矩阵的事实。在此基础上，本文的后半部分通过近似建模和截断的方法推导出了一些迹线公式，这些公式在大多数实际FDLCP系统中是可以数值实现的。数值例子说明了所提出的迹公式的有效性。
In the former part of this paper, a trace formula is established for the H 2 norms of a class of finite-dimensional linear continuous-time periodic (FDLCP) systems based on the solution of the harmonic Lyapunov equations. This trace formula is quite similar in form to what we have for the H 2 norm of an LTI continuous-time system apart from the fact that infinite-dimensional matrices are involved in the FDLCP setting. Based on this formula, in the latter part of this paper some trace formulas are developed via the approximate modelling and truncating approach, which are numerically implementable in most practical FDLCP systems. There are numerical examples to illustrate the efficacy of the trace formulas suggested.