Introducing a New High-Order Chaotic System with an Equilibrium Point and Stabilizing It Using LQR Controller

In this paper, a new high-order chaotic system is proposed. This system has an equilibrium point on center and its specific feature is existence of two large Lyapunov exponents compared to other high-order chaotic systems. In order to prove the existence of high-order chaos in this system, criteria such as energy dissipation of the system, instability of equilibrium point, system absorption and Lyapunov exponents of system are used. Investigating the mentioned criteria confirms the existence of chaos in the system under study. Then, by changing system parameters, different dynamic behaviors such as the limit cycle and high-order chaos can be observed in the system. Finally, using a Linear Quadratic Regulator (LQR) controller, chaotic system’s stability around equilibrium point is guaranteed.