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Abstract and Applied Analysis
Volume 2014, Article ID 471481, 14 pages
http://dx.doi.org/10.1155/2014/471481
Research Article

Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

1School of Transportation and Automotive Engineering, Xihua University, Chengdu 610039, China
2State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

Received 29 March 2014; Revised 8 May 2014; Accepted 8 May 2014; Published 15 June 2014

Academic Editor: Hongli Dong

Copyright © 2014 Xiaohui Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.