Adaptive stabilization of not necessarily minimum phase plants

Abstract We show that a first-order adaptive regulator can stabilize any linear time-invariant plant (LTI) whose transfer function has arbitrary relative degree and order, and is not necessarily minimum phase, provided the dominant slow part of the plant is minimum phase and of relative degree one and the parasitic fast part is stable. The results are extended to r × r multivariable systems whose dominant parts are minimum phase and the spectrum of their high-frequency gains is either in Re[ s ] s ] > 0, and their parasitic fast parts are stable.