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This chapter studies the 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 cost function with guaranteed upper bound for the continuous and discrete case and also an extension for robust control is developed. Numerical examples are included to show the effectiveness of the proposed result.

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