Adaptive control for stabilizing possibly inversely unstable continuous-time plants by using multirate input and fractional-order holds

This paper presents an adaptive control strategy for stabilizing a potentially non-inversely stable, linear and time-invariant plant. Such a strategy consists of a discretization of the plant by means of a fractional-order hold (FROH) with a multirate input in order to place the zeros of the discretized plant into the stability region. In this way, an adaptive controller can be designed so that the discretized plant asymptotically matches a stable reference model without any linking between the reference model zeros and those of the discretized plant. Such a controller ensures the matching of the reference model at sampling instants and the boundedness of the plant output for all time. An example is presented to illustrate this control strategy