Robust stability analysis for nonlinear sampled-data control systems and the Aizerman conjecture

The robust stability condition for sampled-data control systems with sector nonlinearity was presented in our previous paper. Although it is applicable only to the sampled-data control system of a certain class! a usual discrete-time control system can belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. This paper focuses primarily on robust stability in order to analyze a nonlinear element by the linear gain band! in other words, the validity of the Aizerman conjecture extended into discrete-time systems.