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The Kalman-Yakubovich-Popov Lemma in a behavioural framework

✍ Scribed by Robert van der Geest; Harry Trentelman

Book ID
104301083
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
498 KB
Volume
32
Category
Article
ISSN
0167-6911

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✦ Synopsis

The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality. In this paper we derive the KYP Lemma for linear systems described by higher-order differential equations. The result is an LMI in terms of the original coefficients in which the dissipativity problem is posed. Subsequently we study the connection between dissipativity and spectral factorization of polynomial matrices. This enables us to derive a new algorithm for polynomial spectral factorization in terms of an LMI in the coefficients of a polynomial matrix. @ 1997 Elsevier Science B.V.

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✍ Rolf Johansson; Anders Robertsson 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 267 KB

## Abstract This paper presents theory related to stability analysis and stability criteria relevant for observer‐based feedback control systems. To this purpose, a special formulation of the Yakubovich–Kalman–Popov (YKP) lemma is provided. We exploit that controllability is not necessary for exist