Popov-Type Criterion for Stability of Nonlinear Sampled-Data Systems

This paper studies input/output stability of nonlinear sampled-data systems with a sector nonlinearity. A stability condition of circle-criterion type was derived recently, 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. An illustrative example is also given.

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