LMI synthesis of H2 and mixed H2/H∞ controllers for singular systems

This paper considers the H2 control problems for continuous-time singular systems with and without an H∞ constraint. Without the constraint, we derive necessary and sufficient conditions for the existence of H2 output feedback controllers using the linear matrix inequality (LMI) approach. With the H∞ constraint, sufficient LMI conditions on the existence of the H2 controller are obtained. In both cases, the desired H2 controller can be constructed through the feasible solutions of the LMIs. The proposed synthesis method is illustrated through numerical examples.published_or_final_versio