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 externally positive 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.