Stable approximation of time-variable systems

The authors previously introduced the notion of a “uniformly balanced” realization for time-variable systems. Thi s representation is charac terized by the fact that its control labi1ity and observability grammians are equal and diagonal. Such a framework has many remarkable properties and leads to a setting where the subsystems can be taken as reduced model for time-variable systems. It turns out that once the stabi1ity of a subsystem is guaranteed, then the subsystem preserves many of the properties of the original system. In this paper the stability of subsystems is fully explored