Dynamic partial state-feedback revisited for output tracking using Lyapunov redesign and model-following control

We study the problem of dynamic partial state-feedback trajectory tracking for a class of minimumphase nonlinear systems in Byrnes-Isidori form using the Lyapunov redesign technique. We use an estimate of the unknown internal state in the feedback linearising control resulting in a dynamic control law. We consider three different approaches, namely, a simulation of the internal dynamics, an observer for the internal state, and model following control (MFC). Each design achieves asymptotic tracking. The observer-based approach and the MFC do so while overcoming the typical problem of unbounded discontinuous control signals if a sufficiently accurate estimate of the initial state of the process is available. Both approaches allow for asymptotic tracking with a continuous control signal if the initial state of the process is known. We demonstrate the tracking capabilities by a numerical example.