ON CONSTRUCTION OF NON-SMOOTH LYAPUNOV FUNCTIONS FOR NON-SMOOTH SYSTEMS

摘要

Lyapunov's stability theory has been extended to the stability analysis of non-smooth systems in which non-smooth Lyapunov functions are often constructed. It is believed that the main difficulty in Lyapunov stability analysis of non-smooth systems is the determination of the generalized derivative on a discontinuity surface, which involves the estimation of the intersection of a number of convex sets. Although in this work, it still requires above determination, the form of the sets is simplified, and the number of the sets involved in the generalized derivative is significantly reduced as compared with previous work by Shevitz and Paden (1994). The current extension does not require much advanced mathematical machinery and therefore, makes the stability analysis of non-smooth systems practically easier. Two examples, including a system with stick-slip friction and a robotic system having interaction with the environment, are used to demonstrate the applicability of the method proposed in this paper.