An algebraic framework for quadratic invariance

In this paper, we present a general algebraic framework for analysing decentralized control systems. We consider systems defined by linear fractional functions over a commutative ring. This provides a general algebraic formulation and proof of the main results of quadratic invariance, as well as naturally covering rational multivariable systems, systems with delays, and multidimensional systems. The approach extends to the extended class of internally quadratically invariant systems.