Comments on "Some Conditions on Zeros to Avoid Step-Response Extrema"-Part I1

This paper gives a correct version of Theorem 2 of the above-mentioned paper.’ In Theorem 2 of the above-mentioned paper,’ relation R is defined as inequality, and it gives two more conditions. In the theorem, however, relation R has to be defined as a one-to-one correspondence relationship since the theorem deals with finite and infinite zeros. In this case, the number of zeros is the same as that of poles. some trivial results which seemed unknown as can be seen from very recent related works [ 5 ] , [61. Nevertheless, the author believes that the results in [1]-[4] are given in an ad hoc manner and that, in contrast, Theorem 2 in the paper gives the designer a better insight and a systematic way by means of the system’s poles and zeros. Although the intention should have been clear from the context of the paper, we give a new statement of Theorem 2 in light of the second comment. Theorem 2: Let G(s) be an irreducible transfer function with r i finite and infinite stable zeros zz{l<z<n: and n real stable poles p J ST% ) , Then the step-response of G ( s ) has no extremum for t > 0 if there exists a one-to-one correpondance R satifying the following condition: