Exponentially stabilizing adaptive control for linear slowly time-varying systems

This work presents some results pertaining to the parameter estimation and adaptive control of a linear time-varying system without disturbance or unmodelled dynamics. The system is assumed to be uniformly controllable with known orders, and that its parameters vary asymptotically slowly in the mean within a bounded set. Explicit knowledge of the bounded set is not required. The work adopts the self-excitation technique for estimation, with an exponentially convergent normalization factor in the gradient estimation algorithm. An indirect deadbeat-based adaptive controller is utilized for stabilization. It is shown that the closed loop signals converge exponentially to zero with sufficiently small parameter variations. Copyright (C) 1998 IFAC.