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Mathematical Problems in Engineering
Volume 2015, Article ID 206162, 12 pages
Research Article

Global Asymptotic Stabilization Control for a Class of Nonlinear Systems with Dynamic Uncertainties

1School of Science, Shandong Jianzhu University, Jinan 250101, China
2School of Automation, Southeast University, Nanjing 210096, China

Received 11 May 2015; Accepted 16 August 2015

Academic Editor: Uchechukwu E. Vincent

Copyright © 2015 Jiangbo Yu 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.


This paper is concerned with the global asymptotic stabilization control problem for a class of nonlinear systems with input-to-state stable (ISS) dynamic uncertainties and uncertain time-varying control coefficients. Unlike the existing works, the ISS dynamic uncertainty is characterized by the uncertain supply rates. By using the backstepping control approach, a systematic controller design procedure is developed. The designed control law can guarantee that the system states are asymptotically regulated to the origin from any initial conditions and the other signals are bounded in closed-loop systems. Moreover, it is shown that, under some additional conditions, a linear control law can be designed by the proposed methodology. The simulation example demonstrates its effectiveness.