An adaptive controller which provides Lyapunov stability

An adaptive controller that can provide exponential Lyapunov stability for an unknown linear time-invariant (LTI) system is presented. The only required a priori information about the plant is that the order of an LTI stabilizing compensator be known, although this can be reduced to assuming only that the plant is stabilizable and detectable at the expense of using a more complicated controller. This result extends the work of M. Fu and B.R. Barmish (see ibid., vol.AC-31, p.1097-1103, Dec. 1986) in which it is shown that there exists an adaptive controller which provides exponential Lyapunov stability if it is assumed that an upper bound on the plant order is known and that the plant lies in a known compact set; it shows that adaptive stabilization is possible under very mild assumptions without large state deviations