Robust stability for nonlinear sampled-data control systems and Aizerman's conjecture

The robust stability criterion for sampled-data control systems with a 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 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 the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.