Minimum sensitivity realizations of networks of linear systems
Uwe Helmke, Michael Schnlein · Numerical Algebra Control and Optimization · 2016
We investigate networks of linear control systems that are interconnected bya fixed network topology. A new class ofsensitivity Gramians is introduced whose singular values measure thesensitivity of the network. We characterize the state spacerealizations of the interconnected node transfer functions suchthat the overall network has minimum sensitivity. We also develop an optimization approach to thesum of traces of the sensitivity Gramians thatdetermine minimum sensitivity state space realizations of thenetwork. Our work extends previouswork by [6,10,11] on$L^2$-minimum sensitivity design.