Algebraic theory for robust stability of interconnected systems: Necessary and sufficient conditions

Abstract
We consider an interconnected system Somade of linear mulrivariable subsystems which are specified by matrix fractions with elements in a ring of stable scalar transfer functions . Given that the th subsystem is perturbed from to and that the system Sois -stable, we derive a computationally efficient necessary and sufficient condition for the -stability, of the perturbed system. These fractional perturbations are more general than the conventional additive and multiplicative perturbations. The result is generalized to handle simultaneous perturbations of two or more subsystems.