Impulsive control of single-mode laser chaotic system

Abstract

In nonlinear optics, single mode laser is a typical example occurring self-organization phenomenon of bistability, oscillation and chaos. Stability analysis and stabilization problem in nonlinear optical systems are problems of great interest. With the development of control theory, impulsive control becomes more and more attractive. Impulsive control can describe some control process which can be used to control the population of a kind of insects by leaving its natural enemies at some proper instant and control the process of reaction by adding chemicals which instantaneously change state variables in a chemical reactor and so on. This paper studies the stabilization problem of single mode laser chaotic system via impulsive control. By using the method of Lyapunov functions, we derive some sufficient conditions for impulsive stabilization. These results are then applied to the single mode laser chaotic system. It is shown that by employing impulsive control method, all the solutions of this kind of chaotic system will converge to an equilibrium point. Finally, some numerical simulation is given to illustrate the efficiency of the obtained results.