On sequences of Hurwitz polynomials related to orthogonal polynomials

On Robust Stability for Hurwitz Polynomials via Recurrence Relations and Linear Combinations of Orthogonal Polynomials

“…Any pair of sequences a n 􏼈 􏼉 n ≥ 0 , b n 􏼈 􏼉 n ≥ 0 satisfying those conditions are said to generate the chain sequence a n /(b n b n− 1 ) 􏼈 􏼉 n ≥ 1 . As a particular case, this occurs when a n 􏼈 􏼉 n ≥ 0 and b n 􏼈 􏼉 n ≥ 0 are chosen in such a way that a n /(b n b n− 1 ) � k for some fixed k satisfying 0 < k ≤ 1/4 (see [24,26]). Notice that in this case we have g n � 1/2 for every n ≥ 0.…”

New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

“…Conversely, it is possible to construct a Hurwitz polynomial by using orthogonal polynomials. For more details, we refer the reader to [20,[30][31][32][33] and, more recently, [34]. In the latter, the authors construct sequences of Hurwitz polynomials from a sequence of orthogonal polynomials, and show several algebraic properties of the constructed family.…”

Robust Stability of Hurwitz Polynomials Associated with Modified Classical Weights

“…To get our results, we follow the ideas in the recent paper [6]. Therein, the authors derived explicit connection formulas between SMOP (with respect to weights supported on positive intervals of the real line) and Hurwitz polynomials.…”

“…M for every n ∈ N, then the sequence { n } n 1 of Hurwitz polynomials constructed via Proposition 3 with b n = b > M satisfies [6]…”

“…The structure of the manuscript is as follows. Section 2 is devoted to a basic introduction of orthogonal polynomials and their relationship with Hurwitz polynomials, as given in [6]. In Section 3 we introduce sequences of Laguerre-type and Jacobi-type orthogonal polynomials by means of the introduction of a parameter t on the orthogonality weight, and obtain algebraic properties related to their zeros.…”