A method for verifying sector conditions in nonlinear discrete-time control systems

The stability of a discrete feedback system with a continuous broken-line nonlinearity is considered. Many nonlinearities in practice are included in this class. Sufficient conditions for this type of nonlinear feedback system to be asymptotically stable in the large are developed using the contraction mapping theory. It is then shown that Kalman's conjecture (1957) for a feedback system with a sector nonlinearity also applies to discrete systems under a restricted sector condition. A method for obtaining this restricted sector by solving a quadratic equation is presented.<
>