Alternate-continuous-control systems with double-impulse.

We propose a mathematical model that can control the stability of an unstable system. Periodicity is an important feature of the system. We add a continuous control to the first half of each period of the system and then add an impulse control J1 at the $1/2$ period time. Again, we do not control the rest half of each period of the system. Finally, we add an impulse control J2 at the end of each period of the system. The system is called an alternate-continuous-control system with double-impulse. We study the stability of the current system by constructing the Lyapunov function. Using the proposed method, we can control the Chua oscillator. The system has two impulse inputs per period, which is more in line with natural law than the system that only has a single-impulse input. Therefore, the system proposed in this paper is more practical than current mature control systems. [ABSTRACT FROM AUTHOR]