A behavioral approach to balanced representations of dynamical systems

Abstract

The behavioral approach to linear systems provides an alternative framework for studying the notion of balanced representations. A new definition for balanced representations is proposed that is one-to-one related to a set of system invariants that is obtained by assuming a specific Hilbert space structure on the system behavior. This notion of balancing is more general than the prevailing notion of balancing in that it is well defined for nonstable systems and is independent of a particular (input-output) representation of the system. It is shown that Lyapunov, LQ̧G, and H ∞ balanced representations are obtained as a special case. An application for the problem of model approximation is discussed.