Zero dynamics for a class of robustly stable polynomials

An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials

“…Although we have only considered the case with one parameter λ, our approach can be used for an arbitrary number of parameters, and the only difficulty would be in solving inequalities with a larger number of parameters. Moreover, we use some known families of robustly stable polynomials to illustrate the algorithm, but the methods presented in [17][18][19] provide great flexibility to generate Schur and Hurwitz robustly stable polynomials in different ways, and this approach can be used with all of them. Finally, the proposed method for Hurwitz polynomials is based in the Möbius transformation relating the unit disk with the left halfplane, and this approach introduces some restrictions on the regions where the zeros are to be located, as explained in the discussion after Example 4.…”

“…Indeed, the location of the roots is directly related to the performance of the system. It is important to notice that some families of robustly stable polynomials (defined in terms of orthogonal polynomials) have been proposed in the literature [17][18][19], and the behavior of the roots in terms of the uncertain parameter has been studied [19].…”

“…Orthogonal polynomials on the unit circle have been recently used in [19] to build families of robustly stable Schur polynomials by using two different approaches:…”

“…Furthermore, we are only considering the situation where there is only one uncertain parameter λ, i.e., d = 1 in Definition 1. More details can be found in [19].…”