A note on the existence of a solution and stability for Lipschitz discrete-time descriptor systems

This paper addresses the existence and uniqueness of a solution and stability for Lipschitz discrete-time descriptor systems. By means of the fixed point principle, a criterion is presented via a matrix inequality, and the criterion guarantees the existence and uniqueness of a solution. In addition, a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously. It is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system. Finally, the approach is illustrated by a numerical example.