In this paper, we examine the application of the well-known hysteresis switching algorithm of adaptive control in the case of a continuously parameterised set of candidate controllers. Subject to existence of a feasible controller in the set, we prove that if the performance functions used at each time by the hysteresis algorithm are selected to be uniformly positive definite in the controller parameters, then one may safely set the hysteresis constant to zero without inducing chattering instability, and ensuring convergence to a performance-optimising controller. Expanding preliminary version of our work that we presented at the 2011 American Control Conference, the present paper adds new numerical simulation examples to demonstrate the application and benefit of the theory.