The Kalman-Yakubovich-Popov inequality for discrete time systems of infinite dimension

被引：0

作者：

Arov, D. Z. ^{[1
]}

Kaashoek, M. A.

Pik, D. R.

机构：

[1] S Ukranian Pedag Univ, Phys Math Inst, Dept Math Anal, UA-65020 Odessa, Ukraine

[2] Leiden Univ, Fac Sci, Math Inst, NL-2333 CA Leiden, Netherlands

[3] Vrije Univ Amsterdam, Fac Sci, Dept Math, NL-1081 HV Amsterdam, Netherlands

来源：

JOURNAL OF OPERATOR THEORY | 2006年 / 55卷 / 02期

关键词：

dissipative linear systems; optimal control; stability;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Infinite dimensional discrete time dissipative scattering systems are introduced in terms of generalized (possibly unbounded) solutions of the Kalman-Yakubovich-Popov inequality (KYP-inequality). It is shown that for a minimal system the KYP-inequality has a generalized solution if and only if the transfer function of the system coincides with a Schur class function theta in a neighborhood of zero. The set of solutions of the KYP-inequality, its order structure, and the corresponding contractive systems are studied in terms of theta. Also using the KYP-inequality a number of stability theorems are derived.

引用

页码：393 / 438

页数：46

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