Piecewise constant high-gain adaptive lambda-tracking for higher relative degree linear systems

In this paper we present an adaptive high-gain observer-based controller for linear, minimum-phase systems with known relative degree larger than one and known sign of the high-frequency gain. The adaptation scheme does not use any identification mechanism and is universal in the sense that it is independent of the system the controller is designed for. We prove that for any bounded and sufficiently smooth reference signal the modulus of the tracking error becomes smaller than an arbitrary small but fixed error bound lambda if t tends to infinity. All states of the nonlinear closed-loop system remain bounded