The stability of impulsive incommensurate fractional order chaotic systems with Caputo derivative

A Novel Fast Convergence Control Scheme for a Class of 3D Chaotic Systems with Uncertain Parameters and External Disturbances

“…where u 0 is the controller to be designed such that the equilibrium point (0, 0, 0) of system (2) is asymptotically stable. e purpose of considering system (2) firstly is that through designing controller u 0 , one can get the analytical solution of system (2). By using the obtained analytical solution, we can easily construct the Lyapunov function which is helpful in proving eorem 2.…”

“…According to (14), we know that if u 0 is taken as (15), then equation (11) is the solution of system (2). From (11), it is obvious that the equilibrium point (0, 0, 0) of system (2) is asymptotically stable.…”

“…A system is called as the chaotic system, provided that it exhibits chaos phenomenon. Due to its powerful potential applications in secure communications, biological systems, information processing, etc., the control of chaotic system has attracted extensive attention of scholars in recent 20 years, and many e cient approaches have been presented for controlling chaos, such as OGY control [1], impulsive control [2], fuzzy control [3,4], sliding mode control [5,6], adaptive control [7,8], composite learning control [9,10], and so on. Nowadays, many papers about controlling chaotic systems have been published.…”

The Exponential Stabilization of a Class of n‐D Chaotic Systems via the Exact Solution Method

“…Now, it is generally agreed that this complex and irregular phenomenon is useful because it has many applications in some areas such as secure communications and information sciences [1]. For the purpose of utilizing chaotic signals, the chaos control and chaos synchronization of dynamical systems have attracted a wide range of research activities for over two decades [2][3][4][5][6][7][8]. A wide variety of approaches have been proposed for achieving chaos control and synchronization which include adaptive control method [9], sliding mode control [10,11], predictive control method [12], and backstepping method [13].…”

Fractional-order control systems - theory and applications

“…An adaptive controller is proposed in [108] to achieve stabilization of a three-dimensional incommensurate fractional-order chaotic system with an assumption that its first subsystem is asymptotically stable without any control effort. In [109], the stabilization of a class of incommensurate fractionalorder chaotic systems is realized via an impulsive control approach. Nevertheless, neither system uncertainties nor external disturbances are considered in both mentioned works, while the asymptotic stability of incommensurate fractional-order chaotic systems in the presence of uncertainty and disturbance is guaranteed by utilizing a discontinuous adaptive sliding mode controller, as presented in [110].…”