Explicit Representation For Solutions Of A Kind Of Singular Linear Differential Algebraic Equations

Differential algebraic equations (DAEs) have a wide application, such as power systems and interconnected systems, which can be characterized by the differential algebraic systems. In the paper, we study and present a new generalized inverse E+for rectangular matrices based on projections, which includes known generalized inverses as a special case, such as the Moore Penrose inverse and Drazin inverse. We give the necessary and sufficient condition for the existence of the generalized inverse, which is a generalization of related theorem in [16]. For regular matrix pencils (E, A), we present a representation of E+by Weierstrass canonical form, and discuss the difference between E+and ED. In addition, the existence of solutions for a class of singular linear DAEs is discussed by using{2}-inverse with given range and null space. Besides, we give an explicit representation of the solutions of linear differential algebraic systems, which satisfies different consistent conditions.