Abstract: This paper addresses certain inherent limitations of
local priority hysteresis switching logic. Our main result establishes
that under persistent excitation assumption, it is possible to
relax constraints requiring strict positivity of local priority and
hysteresis switching constants. Relaxing these constraints allows the
adaptive system to reach optimality which implies the performance
improvement. The unconstrained local priority hysteresis switching
logic is examined and conditions for global convergence are derived.