Gramian-preserving frequency transformation for linear continuous-time state-space systems

This paper proposes a new expression of frequency transformation for linear continuous-time state-space systems. The proposed frequency transformation preserves the controllability Gramian and the observability Gramian of prototype state-space systems, and thus allows us to easily realize various kinds of state-space systems keeping the same realization as that of prototype state-space systems. Our result is derived from a modified state-space formulation of frequency transformation and an appropriate state-space representation of reactance functions