Estimations of Ultimate Bounds for the PRT System and Its Application in Chaos Synchronization

This paper is concerned with the ultimate bounds and positively invariant sets for a system describing the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. Based on generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive a new ellipsoidal estimate and a cylindrical domain of the globally exponentially attractive set and positively invariant set for the PRT system via the generalized Lyapunov function theory. In addition, linear feedback control with both two states and two inputs is proposed to realize the globally exponential synchronization of two PRT systems via inequality techniques. Some sufficient algebraic criteria for the globally exponential synchronization of two PRT chaotic systems are obtained analytically. Numerical simulations are presented to show the effectiveness of the method.