INPUT TO STATE STABILIZABILITY FOR PARAMETRIZED FAMILIES OF SYSTEMS

This paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications . A Lyapunov-theoretic necessary and sufficient characterization is ob tained for a natural notion of robust uniform set stability; this char acterization allows replacing ad hoc conditions found in the literatur e by more conceptual stability notions. We then use these techniques t o establish a result linking state-space stability to 'input to state' (bounded-input bounded-state) stability. In addition, the preservatio n of stabilizability under certain types of cascade interconnections i s analysed.