Abstract
This chapter studies the H-2 control problem for linear singular systems. Firstly a proportional plus derivative feedback controller for continuous and discrete cases for descriptor systems is given, satisfying the closed loop systems normal and stable states. A necessary and sufficient condition for the solvability of this problem should be obtained in terms of linear matrix inequality. In second part, the designed controller is required to yield a H-2 cost function with guaranteed upper bound for the continuous and discrete case and also an extension for robust H-2 control is developed. Numerical examples are included to show the effectiveness of the proposed result.