Indirect method for adaptive control

An indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed. In a rigorous analysis, Lyapunov stability of the resulting closed loop system (without the need for external excitation), possible global instabilities, as well as global convergence subject to sufficient excitation, are shown. Moreover, the behaviour of the closed loop system is analysed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order, contains slight nonlinearities and time variation effects, and is subject to plant and measurement disturbances.