The Fractional Complex Order Plant model, which has lately gained popularity in applied physics and control systems, is the main subject of this study. The major contribution of this study to the literature is the discussion of the physical phenomena of complex plant models and how they affect the stability and robustness of the systems. Because the Fractional Complex Order Plant model is the most general mathematical form, other plant models covering the Integer Order Plant and the Fractional Order Plant can be easily created with this benefit. The proposed approach using the classical Proportional Integral controller which is recalled as the Integer-Order PI controller in this paper gives the calculation equations of the physical alterations of plants having integer, fractional, and complex orders. Along with the visuals and with the aid of simulations, the consequences of the parameters on the system are described. Additionally, the advantages and disadvantages of the proposed controller designs for each of the three plant species are discussed.
For continuous-time complex-valued neural networks, this paper addresses the state-feedback stabilization issue via dynamic event-triggered protocol. Aiming at random parameters' switching, semi-Markov jump model surpasses the Markov jump model in terms of its generality, enabling us to effectively capture the occurrence of random abrupt alterations in both the structure and parameters of complex-valued neural networks. To optimize packet transmission, a new dynamic event-based protocol is introduced to judge whether the previous signal transmission continues. The design of this protocol takes into full consideration the imaginary part characteristics of the system, while also integrating the system modes and dynamic variables. Utilizing an appropriate Lyapunov functional that contains auxiliary internal dynamical variables, the desired stability is proposed. Eventually, the effectiveness of theoretical findings is ultimately validated through two numerical simulations.