Generalized Differential Balancing for Variationally Symmetric Systems

In this paper, we introduce the notion of variational symmetry for nonlinear prolonged systems (a variational extension of a nonlinear system) by using corresponding variational systems and by developing the recently introduced generalized differential balancing method for this type of system. Generalized differential balancing is proposed for model reduction of nonlinear systems in the contraction framework and is based on solutions to two nonlinear differential matrix inequalities. Our aim of this paper is to show that for variationally symmetric systems, these two inequalities reduce to one inequality. Finally, we show that variational symmetry is preserved under generalized balanced truncation if the variational Hankel singular values are distinct. (C) 2016 IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.