Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters

New results for an established for the global asymptotic stability of the equilibrium x=0 of nth order discrete-time systems with state saturations, x(k+1)=sat(Ax(k)), utilizing a class of positive definite and radially unbounded Lyapunov functions, v. When v is a quadratic form, necessary and sufficient conditions are obtained under which positive definite matrices H can be used to generate a Lyapunov function v(w)=w/sup T/Hw with the properties that v(Aw(k)) is negative semidefinite, and that v(sat(w))>