Practical impulsive synchronization of chaotic systems with parametric uncertainty and mismatch

Chaotic communication systems in the presence of parametric uncertainty and mismatch

“…From (6) and (8) and the proof given in [10], it can be shown that e(t) 0 , ∀t T N where T N is a sufficiently large constant.…”

Impulsive synchronization of chaotic Lur'e systems via partial states

“…In [2], the stability theory of impulsive differential equations [3] were first applied to design impulsive control law to synchronize two identical chaotic systems. Since then, impulsive control method for synchronization of chaotic systems have received increasing interests and a lot of research works have been accumulated, see [4][5][6][7][8][9][10][11][12][13][14]. The main idea of impulsive control method is to suppress the states of the system at discrete time instants.…”

“…The advantage of impulsive control scheme for synchronization of chaotic systems lies in that only the synchronization impulses are sent to the driven system at the impulsive instants, which can decrease the information redundancy in the transmitted signal and increase robustness against the disturbances. However, in the most existing impulsive synchronization results [2][3][4][5][6][7][8][9][10][11][12][13], the impulsive control input is always exerted on all the states of the driven system, which means that knowledge of the full state information of the driven system is needed. In practice, some states of the driven system are often not available, not measurable or too expensive to measure.…”

Impulsive control of projective synchronization in chaotic systems

“…Because impulsive control allows the stabilization and synchronization of chaotic systems using only small control impulses, it has been widely used to stabilize and synchronize chaotic systems [25][26][27][28][29][30][31][32][33][34][35][36][37]. The impulsive control technique is also suitable to deal with systems which cannot endure continuous disturbance.…”