Time-varying systems and crossed products

Abstract

Abstract. Crossed product algebras are proposed as a framework for the study of input-output properties of linear time-varying systems. It is shown that internally stable systems with bounded continuous coefficients have transfer operators in a crossed product and conversely, that the set of all such transfer operators is dense in a crossed product. It is also shown that crossed product algebras admit causal additive decompositions, and allow a generalized frequency-domain representation.