  The stability analysis of a class of discontinuous discrete-time systems is
studied in this paper. The system under study is modeled as a feedback
interconnection of a linear system and a set-valued nonlinearity. An equivalent
representation, based on a constrained optimization problem, is proposed to
represent the set-valued nonlinearity via a collection of linear and quadratic
constraints. Relying on this description and on the use of a generalized
quadratic set-valued Lyapunov functions, sufficient conditions in the form of
linear matrix inequalities for global exponential stability are obtained.
Numerical examples corroborate the theoretical findings.
