Asymptotic stability of systems with partial state saturation nonlinearities

Several sufficient conditions for the global asymptotic stability of the equilibrium x_e=0 of discrete-time dynamical systems which have saturation nonlinearities on part states are established. We utilize a class of positive definite and radially unbounded Lyapunov functions in establishing our results. When using quadratic form Lyapunov functions, our results are very general since they involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for the systems considered herein