The Stability by Linear Approximation of Discrete-Time Nonlinear Singular Systems

Considering a discrete-time nonlinear descriptor system,we construct the structural form and prove a local existence theorem for solutions.The assumptions of the theorem guarantee thatthe first-approximation systemhas a left-invertible linear operatortransforming the system to the structural form convenient for analysis.We obtain sufficient conditions forthe stability of the nonlinear system by linear approximationunder the assumptions thatthe corresponding part of the first-approximation systemis reducible or regular.Also, we address the reducibility and regularityof linear discrete descriptor systems.