Stability of sampled-data systems with a time-invariant memoryless sector nonlinearity

This paper studies input/output stability of nonlinear sampled-data systems with a sector nonlinearity. A circle-criterion type of stability condition was derived previously, for the case where the sector nonlinearity is possibly time-varying and dynamical. In contrast, this paper deals with the case where it is time-invariant and memoryless, and gives a less conservative stability criterion for such a case. It is derived by applying the multiplier technique, and corresponds to the Popov criterion in the continuous-time setting. The arguments make use of the frequency-domain theory of sampled-data systems, and a sort of convexity in the frequency domain plays an important role. A method with the cutting-plane algorithm is provided for finding a multiplier that proves stability