Fractional descriptor standard and positive discrete-time nonlinear systems

A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example