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
I/O
continuity (in the
L_{\infty
sense). We show how stability preserving mappings arise in some applications in a natural way.