An inclusion principle for dynamic systems

The purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems, which is a suitable mathematical framework for comparing systems with different dimensions. The framework offers immediate results in reduced-order modeling and the overlapping decentralized control of complex systems. The presentation, which is limited to linear constant systems, relies on both the matrix algebra (computations) and the geometric elements (structure) to provide a balanced view of the issues involved in the concept of inclusion. The framework is quite broad, and has been used to consider nonlinear and time-varying systems, as well as systems with hereditary and stochastic effects.