Adaptive control design for linear time-varying system based on internal model principle

We propose a new adaptive control system design using internal model principle for a linear system with polynomial function parameters. In this method, we regard system parameters as variable disturbance and design an estimating law using the internal model of the disturbance so that the disturbance can be rejected. Our method has the features that the tracking error can converge to zero. Furthermore, we give a sufficient condition for the stability in terms of a small-gain theorem. We show that our proposed method relaxes the stability condition more than the conventional methods based on the passivity theorem. Finally, we present a numerical simulation to show the effectiveness of our system.