A robust output feedback controller in a discrete time domain

In this paper, we propose an optimization problem with a linear matrix inequality for a robust output feedback controller in a discrete time domain. It is posed as maximizing the allowable uncertainty while satisfying stability condition. A two-step approach was developed first. To improve performance, we also proposed a method of iterating two convex problems over some variable with fixed other variables, which was shown to converge locally. To improve performance further, several heuristic initializations were also considered. We verify the developed theory and performance of the different methods of initialization through numerical evaluations in terms of robustness and stability.