Absolute Stability of Multivariable Lur'e-type Descriptor Systems
Absolute Stability of Multivariable Lur'e-type Descriptor Systems
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DOI：
10.3182/20080706-5-kr-1001.01016
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
T. Wada;M. Ikeda;E. Uezato
中科院分区：
文献类型：
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作者：
T. Wada;M. Ikeda;E. Uezato
摘要本文的目的是得到线性部分用广义系统表示的多变量Lur’型反馈系统的绝对稳定条件及其解的存在性。非线性是不确定的且满足多变量扇形条件，或非线性的一部分满足范数有界条件。因此，该系统可称为多变量Lur'e型描述系统。在已有的关于Lur’型广义系统的研究中，通常将非线性假设为光滑或单变量标量函数集，而本文放宽了光滑假设，考虑了多变量向量值非线性。所得到的稳定性条件用线性矩阵不等式来描述，这是作者先前关于多变量Lur'e系统的扩展波波夫准则的结果的推广，该系统的线性部分用状态空间方程表示。
Abstract The purpose of this paper is to derive conditions for absolute stability as well as existence of solutions for multivariable Lur'e-type feedback systems whose linear part is expressed by a descriptor system. The nonlinearities are uncertain and satisfy multivariable sector conditions, or a part of the nonlinearities satisfies a norm bounded condition. Thus, the systems can be refered to as multivariable Lur'e-type descriptor systems. In the existing works on Lur'e-type descriptor systems, the nonlinearities were assumed to be smooth or given as a set of single-variable scalar functions, while in this paper, the smoothness assumption is relaxed and multivariable vector-valued nonlinearities are considered. The obtained stability conditions are described in terms of linear matrix inequalities, which are extensions of the authors’ previous results on extended Popov criteria for multivariable Lur'e systems whose linear part is expressed by a state-space equation.