Global sliding mode control and application in chaotic systems

Abstract

This paper is concerned with the stabilization problem for a class of nonlinear systems. Using the global sliding mode control approach, a novel robust control law is established to make the state of system stable and to improve the robustness and the stability of system. A new reaching law is introduced to reduce the chattering. Finally, the method is applied to chaotic systems and an example of the chaotic system is given to illustrate the advantage of the proposed method.

Multiple Faults Detection and Isolation via Decentralized Sliding Mode Observer for Reconfigurable Manipulator

“…Yet the global sliding surface [32][33] can drive the system state to the sliding surface at the very beginning, the reaching interval can be eliminated.…”

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

“…In the following, the conditions are derived to evaluate the stability and robustness of the uncertain time-delay chaotic system with input dead-zone nonlinearity (3) restricted to the sliding surface SðtÞ50 with the existence of appropriated positive definite matrices.…”

“…The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system's parameters. Over the past decades, chaos control has been widely investigated and many researches have been studied in this field [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In [1], a linear feedback control method is proposed for controlling uncertain L€ u system.…”

“…In [9], a linear active control technique is developed for the global chaos synchronization problem of two identical chaotic systems and two nonidentical chaotic systems. However, these methods [1][2][3][4][5][6][7][8][9] can not deal with the effects caused by input dead-zone nonlinearity and timedelays. In practice, the problem of input dead-zone nonlinearity and time-delays is often encountered in various engineering systems, and the existence of input dead-zone nonlinearity and time-delays frequently becomes a source of instability and poor performance.…”

“…In practice, the problem of input dead-zone nonlinearity and time-delays is often encountered in various engineering systems, and the existence of input dead-zone nonlinearity and time-delays frequently becomes a source of instability and poor performance. Hence, chaos control with input dead-zone nonlinearity and time-delays is more important than that of without input dead-zone nonlinearity and time-delays [1][2][3][4][5][6][7][8][9].…”