On the aggregation of linear discrete-time invariant stochastic systems

The notion of adaptively aggregating a linear discrete time-invariant large-scale stochastic system is presented. It is shown how the eigenstructure of the aggregated system evolves and gains support consistent with specific characteristics of the system being aggregated and with an aggregation matrix functional defined herein. Necessary conditions for the existence of the aggregation matrix functional for the random system components are given. The uniqueness question is addressed. An aggregation performance measure is defined based on certain mild conditions that are imposed on the targeted large-scale system´s environmental characteristics.