A Graphical Stability Analysis Method for Cascade Conjugate Order Systems

Abstract

Abstract The theory and applications of complex fractional analysis have recently become a hot topic in the fields of mathematics and engineering. Therefore, studies on the complex order systems and their subset called the complex conjugate order systems began to appear in the control community. On the other hand, the concept of stability has always been an important issue, especially in the analysis and control of dynamical systems. In this paper, a graphical method for stability analysis of the complex conjugate order systems is presented. Since the proposed method is based on the Mikhailov stability criterion known from the stability theory of integer order systems, it is named the generalized modified Mikhailov stability criterion. This method gives stability information about the higher order complex conjugate order systems, i.e. cascade conjugate order systems, according to whether it encloses the origin in the complex plane or not. Three simulation examples for the cascade conjugate order systems are given to show the effectiveness and reliability of the method presented. The results are verified by the poles on the first sheet of Riemann surface and also time responses of the systems, which are calculated analytically in a very complex way.