Method of Lyapunov functions for systems with higher-order sliding modes

Authors:
A. E. Polyakov;A. S. Poznyak
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;The Research and Advanced Studies Center of the National Polytechnic Institute (CINVESTAV), Mexico City, Mexico
Venue:
Automation and Remote Control
Year:
2011

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Abstract

For the control systems with higher-order sliding modes, a method was proposed to construct the Lyapunov functions on the basis of the method of characteristics for solution of a special first-order partial derivative equation. Its successful solution enables one to generate the Lyapunov function which proves that the convergence time is finite and estimates explicitly the time of reaching the sliding mode.