Further corrections to "Comments on ́On the Lyapunov matrix equatioń"

The purpose of this correspondence is to point out that the proof of Theorem 3 in the above paper is invalid.     

A note on "Two counterexamples to Aizermańs conjecture"

It is shown that Fitts' third-order counterexample to Aizerman's conjecture is false for some values of the parameters.     

Comments on "Luenbergeŕs canonical form revisited"

Results similar to those presented in the above paper have previously been developed for a slightly different version of Luenberger's canonical form. These results are summarized herein to provide an alternate canonical form that can be used for system identification. For certain applications, such as observer design, the canonical form presented is particularly well suited. Both canonical forms provide the same number of undefined parameters.     

Comments on "Comments on the Routh-Hurwitz criterion"

It is shown that the algorithm given by Shamash for determining the number of roots of polynomial in the right half plane via the Routh table in the presence of purely imaginary roots and a left column zero is not complete and can give erroneous results. Modification for getting correct results is suggested.     

A note on the Routh-Hurwitz criterion

An example belonging to the category where the first entry in a certain row of the Routh array vanishes is presented. The well-known ε-method ceases to be applicable in this example.     

A note on the Routh-Hurwitz test

This note demonstrates how the ε-method in the original Routh-Hurwitz test can be applied when the Routh array contains a row with zero leftmost element together with an all-zero row. The complete root distribution is determined by applying the criterion only once to the given polynomialD(s)without either factoring out a common divisor or shifting the imaginary axis. Since the test may become computationally tedious due to the inclusion of cumbersome ε-terms, the recently reported method of Shamash [1] is used to simplify the computational scheme. This method, being restricted to the case whereD(s)has purely imaginary roots constituting the whole set of roots of the greatest common even divisor, is here refined and generalized to accommodate all cases in which all-zero rows appear.     

Comments on "Numerical application of Szegós method for constructing Liapunov functions"

It is pointed out that the algorithmic method recently suggested by Hewit and Storey for the construction of Lyapunov functions yields a result which is expressible in closed form.