GENERALIZED INVERSES OF DIFFERENTIAL-ALGEBRAIC OPERATORS

In the theoretical treatment of linear differential-algebraic equation s one must deal with inconsistent initial conditions, inconsistent inh omogeneities, and undetermined solution components. Often their occurr ence is excluded by assumptions to allow a theory along the lines of d ifferential equations. This paper aims at a theory that generalizes th e well-known least squares solution of linear algebraic equations to l inear differential-algebraic equations and that fixes a unique solutio n even when the initial conditions or the inhomogeneities are inconsis tent or when undetermined solution components are present. For that a higher index differential-algebraic equation satisfying some mild assu mptions is replaced by a so-called strangeness-free differential-algeb raic equation with the same solution set. The new equation is transfor med into an operator equation and finally generalized inverses are dev eloped for the underlying differential-algebraic operator.