On characterisations of the input to state stability properties for conformable fractional order bilinear systems

Abstract

Abstract This paper proposes for the first time the theoretical requirements that a fractional‐order bilinear system with conformable derivative has to fulfil in order to satisfy different input‐to‐state stability (ISS) properties. Variants of ISS, namely ISS itself, integral ISS, exponential integral ISS, small‐gain ISS, and strong integral ISS for the general class of conformable fractional‐order bilinear systems are investigated providing a set of necessary and sufficient conditions for their existence and then compared. Finally, the correctness of the obtained theoretical results is verified by numerical example.