Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators

This paper is on the design of robust output feedback integral control for minimum-phase nonlinear systems with a well-defined relative degree. Previous work has shown how to design such controllers to achieve asymptotic regulation by a two-step process. First, robust control is designed to bring the trajectories to a small neighborhood of an equilibrium point. Within this neighborhood, the control then acts as a high-gain feedback that stabilizes the equilibrium point. The asymptotic regulation achieved by integral action happens at the expense of degrading the transient performance. In this paper, we present an approach to improve the transient performance. The control design is a continuous sliding mode control with integral action. However, the integrator is introduced in such a way that it provides integral action only ''conditionally'', effectively eliminating the performance degradation. There are two main results in the paper: the first is asymptotic regulation and the second confirms the transient performance improvement by showing that the output feedback continuous sliding-mode control with integral action can be tuned to recover the performance of a state feedback ideal sliding mode control without integral action.