Rank Minimization under LMI constraints: A Framework for Output Feedback Problems

Convex optimisation techniques for solving linear matrix inequalities have been recently applied to robust state-feedback synthesis for uncertain systems. The approach does not seem to extend easily to the output feedback problem. In this paper, we propose a single framework for addressing a number of output feedback stabilization problems for LTI systems. This includes static output feedback stabilization, dynamic reduced-order output-feedback stabilization, reduced-order H 1 synthesis and synthesis with constant scalings.