NUMERICAL-SOLUTION OF DIFFERENTIAL ALGEBRAIC RICCATI-EQUATIONS

We consider Riccati matrix differential algebraic equations arising from singular or descriptor control problems. We discuss the solvability of such equations under different conditions. In order to apply numerical methods for differential algebraic systems one has to transform the equation. Unfortunately, these equations then have a linear part, which is described by a singular pencil, and thus the usual integration methods do not apply. Under some conditions, which we discuss, these singularities can be removed by a preprocessing algorithm, and the equation can then be solved by well-known methods for differential algebraic systems like DASSL of L. Petzold or LIMEX of Deuflhard, Hairer, and Zugck. We discuss the numerical procedures and give some numerical examples. © 1990.