Abstract
In this thesis, the H_infinity control problem and positive real control problem for continuous-time differential-algebraic equations (DAEs) are solved. All the proofs are purely algebraic. Therefore, they are simple and definite. The first part considers H_infinity control problem for DAEs which are not necessarily regular and possibly have impulse modes and/or jw-axis zeros. We show a necessary and sufficient condition for the existence of a proper controller that satisfies a prescribed H_infinity condition as well as stabilizes the closed-loop DAE and eliminates all impulse modes. The parametrization of H_infinity dynamic output feedback controllers is also established. Through the line with the first part, the second part is dedicated to the positive real controller design. We show a necessary and sufficient condition for the existence of a proper controller that renders the closed-loop DAE extended strictly positive real and stable as well as eliminates all impulse modes. The parametrization of positive real controllers is also established.