Linear time-variable systems: Stability of reduced models (Q790772)

The notion of a 'uniformly balanced' realization for time-variable systems has been previously introduced. This representation is characterized by the fact that its controllability 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 stability 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.