When Is a Storage Function a State Function in Discrete Time?
When Is a Storage Function a State Function in Discrete Time?
复制标题
存储函数何时是离散时间的状态函数？
DOI：
10.1137/s0363012900371502
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
T. Fujii
中科院分区：
文献类型：
--
作者：
O. Kaneko;T. Fujii
本文的目的是研究离散时间中存储函数何时是状态函数。如Trentelman和Willems[Systems Control Let.，32(1997)，pp.249-259]，[SIAM J.Control Opti.，36(1998)，pp.1703-1749]所示，每个存储函数都是连续时间中的状态函数。乍一看，同样的说法似乎在离散时间内也成立。与这种预期相反，这通常并不是真的。实际上，与连续时间情形相比，离散时间情形不仅涉及到一些不同于连续时间情形的问题，而且还涉及到一些更为困难的问题。本文准确地解决了这些问题，并证明了每个非负存储函数都是离散时间线性时不变动态系统供给率的状态函数。
The purpose of this paper is to investigate when a storage function is a state function in discrete time. As shown by Trentelman and Willems [Systems Control Lett., 32 (1997), pp. 249--259], [SIAM J. Control Optim., 36 (1998), pp. 1703--1749], every storage function is a state function in continuous time. At first glance, the same claim seems to hold also in discrete time. Contrary to this expectation, this is not true in general. In fact, the discrete time counterpart involves not only some different but also some more difficult issues compared with the continuous time case. This paper addresses these issues exactly and shows that every nonnegative storage function is a state function of a supply rate with a linear time-invariant dynamical system in discrete time.