Index reduction for second order singular systems of difference equations

This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following algebraic approach proposed by Kunkel and Mehrmann for pencils matrix valued functions, first we present a theoretical framework based on procedure reduction analyze solvability initial value problems SiDEs, which followed systems. We also describe methods structural properties related these Namely, two numerical algorithms so-called strangeness-free forms are presented. Two associated index notions introduced discussed. work extends complements some recent results high continuous-time