  This paper provides a first example of constructing Lyapunov functions in a
class of piecewise linear systems with limit cycles. The method of construction
helps analyze and control complex oscillating systems through novel geometric
means. Special attention is stressed upon a problem not formerly solved: to
impose consistent boundary conditions on the Lyapunov function in each linear
region. By successfully solving the problem, the authors construct continuous
Lyapunov functions in the whole state space. It is further demonstrated that
the Lyapunov functions constructed explain for the different bifurcations
leading to the emergence of limit cycle oscillation.
