I suggest looking at Lyapunov's direct method and possibly LaSalle's principle and their nonsmooth extensions.

http://www4.ncsu.edu/~schecter/ma_532_fa12/lasalle.pdf

http://ieeexplore.ieee.org/abstract/document/317122/

I suggest looking at Lyapunov's direct method and possibly LaSalle's principle and their nonsmooth extensions.

https://schecter.math.ncsu.edu/ma_532_fa12/lasalle.pdf

http://ieeexplore.ieee.org/abstract/document/317122/