Minimum sensitivity realizations of networks of linear systems

Uwe  Helmke; Michael  Schönlein

doi:10.3934/naco.2016010

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2016, Volume 6, Issue 3: 241-262. Doi: 10.3934/naco.2016010

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Minimum sensitivity realizations of networks of linear systems

Uwe Helmke^1, and
Michael Schönlein^2,

1.
Institute for Mathematics, University of Würzburg, Emil-Fischer Straße 40, 97074 Würzburg
2.
Institute for Mathematics, University of Würzburg, Emil-Fischer Straße 40, 97074 Würzburg

Received: March 31, 2015

Revised: June 30, 2016

Published: August 2016

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Abstract

We investigate networks of linear control systems that are interconnected by a fixed network topology. A new class of sensitivity Gramians is introduced whose singular values measure the sensitivity of the network. We characterize the state space realizations of the interconnected node transfer functions such that the overall network has minimum sensitivity. We also develop an optimization approach to the sum of traces of the sensitivity Gramians that determine minimum sensitivity state space realizations of the network. Our work extends previous work by [6,10,11] on $L^2$-minimum sensitivity design.

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Mathematics Subject Classification: Primary: 93B35; Secondary: 93C05.

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