Global adaptive pole placement: Detailed analysis of a first-order system

This paper studies a deterministic adaptive pole positioning problem for a linear first-order system. The principal contribution is to specify an adaptive control law which secures global convergence. The key conditions required are that an externally available plant input be persistently exciting, and that an underbound (not necessarily tight) be known on the magnitude of the input coupling gain. The pattern of the solution to the problem can carry over to high-order systems.