Solvability conditions for the positive real lemma equations in the discrete time

被引：1

作者：

Ferrante, Augusto ^{[1
]}

Ntogramatzidis, Lorenzo ^{[2
]}

机构：

[1] Univ Padua, Dipartimento Ingn Informaz, Via Gradenigo 6-B, I-35131 Padua, Italy

[2] Curtin Univ, Dept Math & Stat, Perth, WA, Australia

来源：

IET CONTROL THEORY AND APPLICATIONS | 2017年 / 11卷 / 16期

关键词：

discrete time systems; computability; digital control; transfer functions; matrix algebra; asymptotic stability; solvability conditions; positive real lemma equations; passivity theory; general theory; positive-realness; discrete time; right-invertibility; left-invertibility; transfer function; state matrix; YAKUBOVICH-POPOV LEMMA; FACTORIZATION;

D O I：

10.1049/iet-cta.2017.0314

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Passivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discrete-time positive real lemma appears to be an important issue. While for minimal realisations the relations between passivity, positive-realness and existence of solutions of the positive real lemma equations is very well understood, it seems fair to say that this is not the case in the discrete-time case, especially when the realisation is non-minimal and no conditions are assumed on left- and/or right-invertibility of the transfer function. The purpose of this study is to present a necessary and sufficient condition for existence of solutions of the positive real equations under the only assumption that the state matrix A is asymptotically stable.

引用

页码：2916 / 2920

页数：5

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