Generalized zero sets location and absolute robust stabilization of continuous nonlinear control systems

Abstrad-We describe an analytic method for finding the location of the generalized zero set of a vector-valued function which depends on m real variables and (n + k) complex parameters. The method is applied to a robust design problem of a nonlinear Lurie type continuous-time system, with the linear part under uncertainty conditions. We find the complete feasible set of sectors of the nonlinearities which allows robust absolute stability of the system, according to the Popov criterion. Illustrative numerical examples are provided. intersections of sets