Minimum sensitivity realizations of networks of linear systems | Zendy

Uwe Helmke | Zendy; Michael Schnlein | Zendy

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Minimum sensitivity realizations of networks of linear systems

Author(s) -

Uwe Helmke,

Michael Schnlein

Publication year - 2016

Publication title -

numerical algebra control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.303

H-Index - 20

eISSN - 2155-3289

pISSN - 2155-3297

DOI - 10.3934/naco.2016010

Subject(s) - sensitivity (control systems) , mathematics , topology (electrical circuits) , measure (data warehouse) , state space , node (physics) , state (computer science) , transfer function , control theory (sociology) , network topology , linear system , mathematical optimization , computer science , control (management) , algorithm , combinatorics , mathematical analysis , engineering , statistics , electrical engineering , structural engineering , database , electronic engineering , artificial intelligence , operating system

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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