Robust stability analysis for nonlinear sampled-data control systems in a frequency domain

The robust stability condition 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 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 describes the relationship between the robust stability condition and the Popov criterion for continuous-time system. In addition, this paper shows a representation of an off-axis circle criterion on a complex plane, and proposes an evaluation method of the stability from the relative position with the vector locus of the open loop frequency response characteristics.