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.