to dynamical systems with saturation nonlinearities -- Qualitative theory of control systems with control constraints and state saturation: Two fundamental issues -- Asymptotic stability of dynamical systems with state saturation -- Null controllability of discrete-time dynamical systems with control constraints and state saturation -- Stability analysis of one-dimensional and multidimesional state-space digital filters with overflow nonlinearities -- Criteria for the absence of overflow oscillations in fixed-point digital filters using generalized overflow characteristics -- Stability analysis of state-space realizations for multidimensional filters with overflow nonlinearities -- to part III -- Analysis and synthesis of a class of neural networks with piecewise linear saturation activation functions -- Sparsely interconnected neural networks for associative memories with applications to cellular neural networks -- Robustness analysis of a class sparsely interconnected neural networks with applications to design problem.