Predictive control for constrained discrete-time periodic systems using a time-varying terminal region*

To guarantee stability of a model predictive control scheme it is essential to suitably calculate the terminal region and the terminal penalty term. In this paper we propose an approach to overcome this problem for the class of periodically time-varying systems. We consider both systems with periodic linear dynamics as well as systems with periodic nonlinear dynamics where the nonlinearities can be approximated with polytopic linear differential inclusions. In both cases exploiting the periodicity of the system dynamics leads to linear matrix inequality (LMI) conditions which can be used to calculate the terminal region and the terminal penalty term. The LMI conditions are shown to be less conservative than existing approaches applicable to the considered system class.