A stability theorem of the direct Lyapunov's method for neutral-type systems in a critical case

A new stability theorem of the direct Lyapunov’s method is proposed for neutral-type systems. The main contribution of the proposed theorem is to remove the condition that the D operator is stable. In order to demonstrate the effectiveness, the proposed theorem is used to determine the stability of a neutral-type system in a critical case, i.e. the dominant eigenvalues of the principal neutral term (matrix D in Introduction) lie on the unit circle. This is difficult or infeasible in previous studies.