On Generalized Linear Matrix Difference Systems

G.I. Kalogeropoulos, D.P. Papachristopoulos, S.C. Giotopoulos, and P. Pantazopoulos (Greece)


Matrix Pencils, Canonical Forms, Singular Linear Differ ence Systems


In this paper we consider Generalized Linear Matrix Dif ference Systems of the form: FYk+ρ = GYk, where F, G ∈ Rm×n or Cm×n , ρ ∈ N, and Yk are n ×m atrices, for k = 0, 1, 2, . . .. In case sF − G is a regu lar matrix pencil, using the Weierstrass canonical form, the above system is decomposed in two subsystems whose so lutions are obtained. Moreover the form of the so–called consistent initial condition is given. We also study the case of sF − G being a singular matrix pencil, where, using the Kronecker canonical form, we decompose the system in five subsystems and we obtain the corresponding solutions.

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