Lyapunov Characterizations of Input to Output Stability

This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property, and the results given here extend their validity to the case when the output, but not necessarily the entire internal state, is being regulated. Keywords. Lyapunov functions, output stability, ISS, robust control AMS subject classifications. 93D05, 93D20, 93D09, 34D20 Running Head. Lyapunov Characterizations of Input to Output Stability 1 Introduction This paper concerns itself with systems with outputs of the general form x(t) = f(x(t); u(t)); y(t) = h(x(t)) ; (1) where f : R n \Theta R m ! R n and h : R n ! R p are both locally Lipschitz continuous, f(0; 0) = 0, and h(0) = 0. In the paper [27] (see also [26]), the authors introduced several notions of output stability for such systems. All these notions serve to formalize the idea of ..