Robustification of nonlinear stabilizers in the sample-and-hold sense

It is well known in the literature that stabilization in the sample-and-hold sense is robust with respect to suitably small actuator disturbances. In this paper it is shown that, given a locally bounded steepest descent feedback (continuous or not), induced by a Control Lyapunov Function, the input-to-state stability redesign method can be exploited such that, with a new sampled-data control law, stabilization in the sample-and-hold sense is still guaranteed with arbitrarily large, bounded, actuator disturbance, as long as the bound of the disturbance is known a priori. Observation error is partially allowed too. It is allowed to be arbitrarily large, with a known bound, as long as it does not affect (or affects marginally) the new added control term. The provided results are validated by simulations on a continuous stirred tank chemical reactor.