Generation of stable polytopes of Hurwitz polynomials via Routh parameters

On stable cones of polynomials via reduced Routh parameters

“…Here, we have proved that for continuous-time systems a similar approach can be used via reduced Routh parameters. The results of this paper can be understood as extension of those presented in [3] and [16]. For [3,16], and this paper the multilinear stability condition is the main conception.…”

“…The results of this paper can be understood as extension of those presented in [3] and [16]. For [3,16], and this paper the multilinear stability condition is the main conception. In [16] the method for polytopic approximation of the stability domain is addressed.…”

“…In this paper, we provide the theoretical justification by giving complete proofs. Furthermore, the relevant additional material is added emphasizing relations between papers [3] and [16].…”

“…For [3,16], and this paper the multilinear stability condition is the main conception. In [16] the method for polytopic approximation of the stability domain is addressed. In the conference paper [3] the main idea of conic approximation of the stability domain is considered.…”

“…According to Theorem 3.1, it is possible to draw n stable Routh rays R i (a * ) through an arbitrary stable point a * . In [16] it was shown that if the point is not placed on the boundary of stability domain, then there are positive and negative directions with respect to a * . The positive part of a Routh ray corresponds to α i ∈ (1, ∞) while the negative to α i ∈ (0, 1), and for α i = 1 rays intersect at the point a * .…”