A Corollary for Nonsmooth Systems
  In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function. 
N. Fischer, R. Kamalapurkar, W. E. Dixon
math.OC