On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities
On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities
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关于具有斜率限制非线性系统的稳定因果乘子的存在性
DOI：
10.1109/tac.2009.2031581
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发表时间：
2009
影响因子：
6.8
通讯作者：
I. Postlethwaite
中科院分区：
文献类型：
--
作者：
M. Turner;M. Kerr;I. Postlethwaite
研究了线性时不变（LTI）系统与斜率受限非线性系统的反馈互联的稳定性。与正常治疗这个问题，其中乘数明确选择，然后检查稳定性条件，本技术说明推导出这些乘数的子类的存在条件，即那些是L 1有界的，稳定的，因果关系和秩序等于系统的LTI部分。证明了对于单输入单输出情形，这些存在性条件可以表示为一组线性矩阵不等式，从而可以用现代优化软件有效地求解。实例说明了结果的有效性。
The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are L 1 bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.