Stability and stabilizability of behaviors

Important control theoretic notions like stability, stabilizability and interconnectability of dynamical systems are usually considered in an input-output framework. This paper discusses these concepts for linear dynamical systems in which signal variables are not necessarily decomposed in input and output components but instead play a symmetric role. The behavioral approach provides a suitable axiomatic basis for such a discussion and it is shown that the concepts of stabilizability and interconnectability of dynamical systems allow simple characterizations in terms of the ℓ2 behavior of dynamical systems.