Control systems on regular time scales and their differential rings
Control systems on regular time scales and their differential rings
复制标题
规则时间尺度上的控制系统及其微分环
DOI：
10.1007/s00498-011-0058-7
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Wyrwas
中科院分区：
文献类型：
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作者：
Z. Bartosiewicz;Ü. Kotta;E. Pawłuszewicz;M. Wyrwas
本文描述了定义在非齐次但正则时间尺度上的与非线性控制系统相关的逆差分环的代数构造。在系统是淹没的假设下，构造了系统变量的亚纯函数环，并配备了三个算子(增量导数、纳布拉导数和前移位算子)，研究了它们的性质。发展的形式统一了现有的连续和离散时间非线性系统的理论，也适应了非均匀采样系统的情况。与齐次情形相比，主要困难是Delta(Nabla)导数和移位算子的非对易，以及附加的时间变量出现在微分环的定义中。后者产生的结果是，取决于，必须选择在时间尺度的每个密集点上平滑的反转闭合的新变量。
The paper describes an algebraic construction of the inversive differential ring, associated with a nonlinear control system, defined on a nonhomogeneous but regular time scale. The ring of meromorphic functions in system variables is constructed under the assumption that the system is submersive, and equipped with three operators (delta- and nabla-derivatives, and the forward shift operator) whose properties are studied. The formalism developed unifies the existing theories for continuous- and discrete-time nonlinear systems, and accommodates also the case of non-uniformly sampled systems. Compared with the homogeneous case the main difficulties are noncommutativity of delta (nabla) derivative and shift operators and the fact that the additional time variabletappears in the definition of the differential ring. The latter yields that the new variables of the inversive closure, depending ont, have to be chosen to be smooth at each dense pointtof the time scale.