A Robust Kaiman Conjecture For First-Order Plants

A robust Kaiman conjecture is defined for the robust Lur'e problem. Specifically, it is conjectured that the nonlinearity's slope interval for which robust absolute stability is guaranteed corresponds to the robust interval of the uncertain plant. We verify this robust Kaiman conjecture for first-order plants perturbed by various norm-bounded unstructured uncertainties. The analysis classifies the appropriate stability multipliers required for verification in these cases. Robust control of Lur'e-type nonlinear systems satisfying this novel conjecture can therefore be designed using linear robust control methods.