On stability preserving mappings

We view systems as mappings which connect a set of inputs (input functions) with a set of outputs (output functions). Such systems are said to be stability preserving if a stable (asymptotically stable) reference input results in an output with the same stability properties. In the present paper we study the properties of such mappings, we establish a block diagram algebra for such mappings, and we relate the properties of such mappings to BIBO stability and continuity (in the sense). We show how stability preserving mappings arise in some applications in a natural way.