I. Introduction
Fractional calculus owns a history of more than 300 years. It is a branch of mathematics that deals with noninteger order derivatives and integrals. Compared with integer order calculus, fractional-order integral and derivative can both be treated as weighted integral and thus they have the properties of hereditary and infinite memory [1], [2], which can also be seen from their definitions given in Section II. Such properties give the most significant meaning of fractional-order derivative compared to the integer-order derivative that does not have such properties. Thus, using fractional-order models could better and more accurately describe the characteristics of the real-world systems than integer-order models, as elaborated in [3]–[5]. In the past few years, many researchers have paid significant attention to fractional-order calculus and constructed models for real-world systems, including viscoelasticity, complex systems, neural networks, transmission line, multiagent systems, and so on (see [6]–[10]). Moreover, fractional-order systems, as well as their controls have also been studied in recent years [11]–[13]. However, it is difficult to simply apply the approaches of controller design and analysis developed for integer-order systems to fractional-order systems due to the lack of appropriate mathematical tools. For example, the fractional-order derivative of a composite function is the sum of the infinite number of terms, which is different from the concise closed-form expression of its integer-order derivative easily obtained by applying the chain rule.