Adaptive Stabilization of Discrete-Time Nonminimum Phase Systems

In this paper, we present a direct multirate adaptive control algorithm that ensures global stabilization of a class of (potentially unstable and invertible) linear time-invariant discrete-time plants of known order and relative degree one. An essential feature of our scheme is that no projections are needed, no appeal is made to the persistence of excitation arguments for the stability proof and it has a better transient performance than existing schemes. The implementation of the controller requires some prior information about its Markov parameters, namely, upper and lower bounds on the systems impulse response. It is directly applicable to plants with interlacing real poles and zeros, i.e., with Cauchy index equal to the plant order, provided the adaptation gain is restricted to be smaller than some value determined by the measure of relative primeness of the pole and zero polynomial. This class contains some practically interesting systems, for instance, resistor–inductor or resistance–capacitance circuits.