## 1 Introduction
The stability of the synchronous solution was investigated by using the Lyapunov theory for perturbed systems and the Master-Stability Function approach, and the proposed synchronization scheme was experimentally validated with electronic circuits [34]. In reference [18], a feedback passivity-based controller design for the stabilization of fractional-order unified chaotic systems was proposed, and an adaptive mechanism was also employed such that the controller does not need to know the parameter of the systems. The chaos control and synchronization of fractional financial systems were studied by various control methodologies, such as active control [16], sliding mode control [35], etc. In reference [36], an efficient optimal controller based on [PERSON]'s maximum principle was designed for two identical financial models, and an adaptive controller established by the Lyapunov stability theory was also implemented. Inspired by the above discussions, this paper investigates the dynamical behavior of financial systems, such as their equilibrium points, stability, bifurcation diagrams, and Lyapunov exponents. The consensus of leader-follower multi-agent systems is discussed based on complex financial systems. The main contributions are given as follows:  
1. The dynamic characteristics of the financial system are analyzed, and the results show that the system behavior can be effectively controlled through the parameters of the financial system. 2. According to [PERSON] stability theorem, linear state feedback controllers are designed to synchronize financial systems. Meanwhile, adaptive control laws are derived for synchronization of master-slave systems with unknown parameters, and numerical simulations are given to verify the theoretical results. 3. The consensus theorem of leader-follower multi-agent systems is proved based on complex financial systems. The circuit implementation of master-slave systems consensus is provided through variable synchronization and parameter identification. In this paper, the dynamic behavior of financial systems is first theoretically analyzed, and it is verified through both numerical simulation and circuit implementation. The circuit implementations effectively verify the behaviors of financial system, such as periodic and chaotic behaviors. Secondly, according to the stability theory of master-slave and leader-follower systems, theoretical methods of linear feedback and adaptive control for the consensus of multi-agent systems are proposed based on financial systems. Meanwhile,the feasibility and correctness of the control methods are verified by simulation experiments, and the circuit implementations validate the theoretical results from the perspective of hardware. Different to the references mentioned above, this paper not only studies the linear feedback method to achieve the consensus of master-slave systems with less control costs, but it also investigates parameter identification when the parameters of the master or leader system are unknown. Parameter identification is very important in many practical models when there are some equipment failures or device aging in the actual system. In addition, the theoretical results of master-slave system synchronization and multi-agent consensus are verified through software simulation. Few literature sources propose circuit design for master-slave systems from the perspective of circuit implementation, especially for systems with unknown parameters. Circuit implementation provides a new method for the adaptive synchronization of master-slave systems. The proposed linear feedback control method and parameter adaptive laws can be applied to consensus control for multi-agent systems, and they are useful for practical agents, such as the synchronization and consensus of unmanned systems, smart grids, and mobile robots. In addition, the circuit design for the proposed master-slave systems has important practical value in chaotic secure communication, chaotic cryptography, circuit design and modeling, etc.