Parametric balancing and model reduction for symmetric systems

A class of linear continuous-time minimal realizations with the property of `absolute value´ symmetry of parameters is studied. It is shown that the existence of this realization is a necessary and sufficient condition for a system to be transfer-function-symmetric. To balance the controllability and observability of a symmetric system in the parametric sense, the `parametric balanced realization´ is defined. Some results concerning the determination of this realization as well as its balanced controllability and observability are obtained. To make the balanced controllability and observability `visible´ in the structure of the realization, a `least coupled realization´ is derived from among the `parametric balanced realizations´. A model reduction technique for symmetric systems via the `least coupled realization´ is proposed with an illustrative example