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

In this paper, we propose a new adaptive control system design using internal model principle(IMP) for a linear system with polynomial function parameters. In this method, we regard system parameters as variable disturbance and design an estimating law used the internal model of the disturbance so that the disturbance is able to 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 relax the stability condition more than the conventional methods based on a passivity theorem. Finally, we contain a numerical simulation to show an effect of our system.