A Note on Incremental Stability of Externally Positive Lurie Systems

The Kalman conjecture is shown to be true for Lurie systems in which the linear part is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">externally positive</i> and the nonlinear element satisfies a generalised incremental gain bound. It is shown further that the system satisfies a range of both traditional and incremental stability properties. Multivariable systems are treated in the same framework as single-input-single output systems, giving the results a wider scope than those normally covered by the Kalman conjecture. Some numerical examples illustrate the utility of the results.