STABILIZATION IN SPITE OF MATCHED UNMODELED DYNAMICS AND AN EQUIVALENT DEFINITION OF INPUT-TO-STATE STABILITY

We consider nonlinear systems with input-to-output stable (IOS) unmode led dynamics which are in the ''range'' of the input. Assuming the nom inal system is globally asymptotically stabilizable and a nonlinear sm all-gain condition is satisfied, we propose a rst control law such tha t all solutions of the perturbed system are bounded and the state of t he nominal system is captured by an arbitrarily small neighborhood of the origin. The design of this controller is based on a gain assignmen t result which allows us to prove our statement via a Small-Gain Theor em [JTP, Theorem 2.1]. However, this control law exhibits a high-gain feature for all values. Since this may be undesirable, in a second sta ge we propose another controller with different characteristics in thi s respect. This controller requires more a priori knowledge on the unm odeled dynamics, as it is dynamic and incorporates a signal bounding t he unmodeled effects. However, this is only possible by restraining th e IOS property into the exp-IOS property. Nevertheless, we show that, in the case of input-to-state stability (ISS)-the output is the state itself-ISS and exp-ISS are in fact equivalent properties.