Linear time-variable systems: Balancing and model reduction

A "uniformly balanced" realization for linear time-variable systems is defined. This representation is characterized by the fact that its controllability, and observability Gramians are equal and diagonal. Existence and uniqueness of the uniformly balanced realization is studied. Such a framework has many remarkable properties and leads to a novel method for approximating time-variable systems, where the subsystems of the balanced realization can be taken as a reduced model. The reduced model is examined from the point of view of stability, controllability, and observability.