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.<
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