Robust stabilization of nonminimum-phase systems with uncertainty by sampled-data output feedback

Abstract

Global robust stabilization by sampled-data output feedback is investigated for a family of uncertain nonlinear systems. The nonlinear system under consideration has an interconnect structure, consisting of a driving system and a possibly unstable zero-dynamics with uncertainty, i.e. the driven system. Under a linear growth condition on the uncertain driven system and a Lipschitz condition on the driving system, we prove that there is a sampled-data, output feedback controller globally robustly stabilizing the uncertain nonminimum-phase system. The sampled-data output feedback compensator is designed by emulated versions of continuous-time observer and state feedback law, i.e., by holding the input/output signals constants over each sampling interval. The sampled-data controller consists of a discrete-time observer and controller whose construction relies only on the the nominal part of the system. Global robust stability of the hybrid closed-loop system is shown by feedback domination, together with the robustness of the nominal closed-loop system.