Popov-type criterion for stability of nonlinear sampled-data systems (Q1295053)

The paper deals with pseudo-\(L_2\)-stability of nonlinear sampled-data systems with a sector nonlinearity under the assumption that the nonlinearity in the control system is time invariant and without memory. The authors derive a stability criterion of Popov type by applying the multiplier technique. Since a suitable multiplier that proves stability cannot be found in a graphical manner, they provide a cutting-plane algorithm for finding a multiplier which proves pseudo-\(L_2\)-stability by using a sort of convexity in the frequency domain. A numerical example in which pseudo-\(L_2\)-stability can be proved with the Popov-type criterion but not with the circle-type one is discussed.