Stability of a class of discrete control systems containing a nonlinear gain element

The problem considered in this paper is to find an explicit stability gain sector for a class of autonomous discrete control systems containing a nonlinear gain element. A quadratic form Lyapunov function is assumed and the Aizerman technique [1] is used to find such a stability sector. A method to select the quadratic Lyapunov function to maximize the width of the sector is suggested.