On the Kalman---Yakubovich---Popov lemma and the multidimensional models

Authors:
Olivier Bachelier;Wojciech Paszke;Driss Mehdi
Affiliations:
L.A.I.I., E.S.I.P., University of Poitiers, Poitiers Cedex, France 86022;Control Systems Technology Group, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB;L.A.I.I., E.S.I.P., University of Poitiers, Poitiers Cedex, France 86022
Venue:
Multidimensional Systems and Signal Processing
Year:
2008

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Abstract

This paper focuses on Kalman---Yakubovich---Popov lemma for multidimensional systems described by Roesser model that possibly includes both continuous and discrete dynamics. It is shown that, similarly to the standard 1-D case, this lemma can be studied through the lens of S-procedure. Furthermore, by virtue of this lemma, we will examine robust stability, bounded and positive realness of multidimensional systems.