Abstract
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I/O</tex> continuity (in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_{\infty</tex> sense). We show how stability preserving mappings arise in some applications in a natural way.
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