Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous-time and sampled-data output feedback for a family of nonminimum-phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum-phase systems by a single continuous-time or a sampled-data output feedback controller. The sampled-data output feedback controller is designed by using the emulated versions of a continuous-time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous-time or sampled-data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled-data control, global robust stability of the hybrid closed-loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed-loop system if the sampling time is small enough.