Comments, with reply, on 'Lyapunov stability designs for switching regulator/low-pass filter system' by M.L. Brooks

摘要

Erroneous conclusions reached in the original paper (see ibid., vol.25, no.5, p.602-10, Sept. 1989) concerning the applicability of the Rough criterion in studying the stability of fourth-order linear systems and its relationship with Lyapunov's stability tests are corrected. A brief review of relevant theory is presented, and faults in the analysis that led to these conclusions are identified. The relationship between the Routh criterion and the second method of Lyapunov is reviewed, and a correct application of the Lyapunov method is presented. It is shown that contrary to the conclusions of the paper discussed, these two methods are equivalent for any linear, time-invariant system, including the fourth-order system in question.