Variable structure model reference adaptive control for systems with unknown high frequency gain

In this paper, we consider the design of a variable structure model reference adaptive control (VS-MRAC) for plants with relative degree one without the knowledge of the sign of the plant high frequency gain. A switching method for the control signal, based on an appropriate monitoring function, is proposed. As a result, we show that after a finite number of switchings, the tracking error converges to zero at least exponentially. Interestingly enough, if the initial conditions of some states of the closed-loop system are zero, we show that at most one switching is needed.