Conditional integrator for non-minimum phase nonlinear systems

In this paper we propose a conditional integrator for solving the regulation problem of a class of nonlinear systems that probably possess unstable zero dynamics. The control scheme mainly takes advantage of the auxiliary controller proposed in [3] and a slow integrator. We present that the solution of the regulation problem can be cast as two auxiliary problems. Furthermore it is shown that the design of the conditional integrator requires the design of a feedback control that solves two stabilization problems simultaneously, one inside the boundary layer of a continuously-implemented sliding model control, and one outside it. Hence the design of the auxiliary controller can be independent of the internal model. We approach this issue by using a two-time-scale method. The effectiveness of the controller is illustrated through a linear example.