Learnability of Linear Fractional-Order ILC Systems

The problem of learnability of linear fractional-order systems is investigated, where the systems have the same dimensions of input and output. Firstly, we show from the viewpoint of dissipativity that why a P-type learning algorithm can enable such systems to possess the perfect tracking capability over a finite time interval. Then, two criteria are provided for determining the dissipative property of fractional-order systems. Moreover, the relationship between learnability and strictly positive real is given, it is shown that the strictly positive real implies the learnability of fractional-order systems with an extra condition. Finally, the correctness of the obtained main results is illustrated with an example.