Design of Marx generators as a structured eigenvalue assignment

We consider the design problem for a Marx generator electrical network, a pulsed power generator. We show that the components design can be conveniently cast as a structured real eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Grobner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the real algebraic geometry field. (C) 2014 Elsevier Ltd. All rights reserved.