  We have examined a class of Li\'enard--Levinson--Smith (LLS) system having a
stable limit cycle which demonstrates the case where the LLS theorem cannot be
applied. The problem has been partly raised in a recent communication by Saha
et al., CNSNS 85, 105234 (2020) (last para of sec 4.2.2). Here we have provided
a physical approach to address this problem using the concept of energy
consumption per cycle. We have elaborated the idea through proper demonstration
by considering a generalized model system. Such issues have potential utility
in nonlinear vibration control.
