This paper sets forth general conditions on the existence, boundedness, and proper gains of a control for stabilizing a nonlinear plant state trajectory to a sliding manifold denoted by S contained in the state space as characterized by a smooth quadratic Lyapunov function, V. To state such conditions we define a time-varying (possibly discontinuous in time) state-dependent decision manifold by considering the time-derivative of the quadratic Lyapunov function. The decision manifold disconnects the control space. At each instant of time, stability is achieved by choosing a control in an appropriate half space defined by the decision manifold so that the derivative of the Lyapunov function is negative definite. If the decision manifold moves continuously, then there is no need for a discontinuous (classical VSC) controller unless robustness in the presence of matched disturbances is desired. If the decision manifold is discontinuous, then the need for a discontinuous control is clear. The formulation unifies the various VSC control strategies found in the literature under a single umbrella and suggests new structures. The formulation also provides a simple geometric understanding of the effect of norm bounded but not necessarily matched disturbances and parameter variations on the system. Two examples illustrate the design aspects of the formulation. [S0022-0434(00)02904-X]
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December 2000
Technical Papers
A Unifying Characterization of Robust Sliding Mode Control: A Lyapunov Approach
R. A. DeCarlo,
R. A. DeCarlo
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285
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S. V. Drakunov,
S. V. Drakunov
Department of Electrical and Computer Engineering, Tulane University, New Orlenas, LA 70118-5674
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Xiaoqiu Li
Xiaoqiu Li
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285
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R. A. DeCarlo
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285
S. V. Drakunov
Department of Electrical and Computer Engineering, Tulane University, New Orlenas, LA 70118-5674
Xiaoqiu Li
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division January 31, 2000. Associate Technical Editors: E. Misawa and V. Utkin.
J. Dyn. Sys., Meas., Control. Dec 2000, 122(4): 708-718 (11 pages)
Published Online: January 31, 2000
Article history
Received:
January 31, 2000
Citation
DeCarlo, R. A., Drakunov, S. V., and Li, X. (January 31, 2000). "A Unifying Characterization of Robust Sliding Mode Control: A Lyapunov Approach ." ASME. J. Dyn. Sys., Meas., Control. December 2000; 122(4): 708–718. https://doi.org/10.1115/1.1321267
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