On Singular Linear Matrix Differential Systems

G.I. Kalogeropoulos and I.G. Stratis (Greece)


Matrix Pencils, Canonical Forms, Singular Linear Differ ential Systems, Distributions


In this paper we study Singular Linear Matrix Differential Systems (S.L.M.D.S.) of the form: FY (r) (t) = GY (t), where F, G Rnn or Cnn , r N, sF - G is a reg ular matrix pencil and Y (t) is an n m, r times continu ously differentiable matrix function. Using the Weierstrass canonical form, the above system is decomposed in two subsystems (slow and fast subsystem), whose solutions are obtained. Moreover the form of the socalled consistent initial condition is given, as well as the solution of the sin gular system for an arbitrary initial condition. It includes not only the normal exponential response part which is cre ated by the slow subsystem, but also the impulse part (due to the fast subsystem).

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