Input to state stabilizability for parametrized families of systems

Abstract

Abstract 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 obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state‐space stability to ‘input to state’ (bounded‐input bounded‐state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analysed.