Iterative learning control applied to distributed‐order linear time invariant MIMO systems to achieve learnability

Abstract

Sufficient and necessary conditions for a distributed-order linear time invariant system to be positive real are derived in terms of linear matrix inequalities. The positive realness condition is derived for three of the most usual cases presented in literature, in the realm of distributed-order linear time invariant systems. As an additional product of this paper, the strictly positive realness condition can be derived. In addition, the concept of learnability of fractional-order multi-input multi-output systems is extended to the case of distributed-order systems, which is approached from the concept of output-dissipativity by using an iterative learning scheme.