Necessary Conditions for Schur-Stability of Interval Polynomials

On stable cones of polynomials via reduced Routh parameters

“…, i n−3 = 2, i n−2 = 1, respectively. This yields the first two elements a n 1 , a n 2 of (6) given as a n 1 = w n w n−1 · · · w 2 w 1 , a n 2 = w n−2 w n−3 · · · w 2 w 1 or, using (8), in the simplified form as a n 1 = w n w n−1 · · · w 2 , a n 2 = w n−2 w n−3 · · · w 2 .…”

“…The main problem appearing with the parametric approach is that, in general, the stability domain is nonconvex in the coefficient space. This challenge has led to the development of techniques for convex approximation of the stability domain such as based on ellipsoids [5,9], polytopes [11,14], hyperrectangles [8,12], and convex directions [19]. The type of convex approximation of the stability domain depends on the type of system parameters uncertainty, for example, rectangular approximation is suitable for interval parameters, and polytopic approximation is applicable for polytopic uncertainties.…”

Linear discrete-time systems with fuzzy parametric uncertainty

“…The exception is the case when upper coefficients are fixed [10]. Some more counterparts on application of Kharitonov theorem to Schur stability are given in [11], [12] and [13]. Generally, a subset of exposed edges has to be tested for stability using Segment lemma [14] or using algebraic approach Jury test has to be performed [15].…”

“…Now we will use bilinear transformation (7) to transform discrete-time polynomial (27) into equivalent continuoustime polynomial˜( ) (8). Using the -cut representation (10) and notation (13) We are now looking for minimum preserving stability of polytope (13). The corresponding frequency plot of ( ) is shown in Fig.…”

Stable polytope of reflection vector sets

“…Much research work has been done to approximate the Schur stability domain by boxes [3]- [4], by ellipsoids [5]- [6] , by polytopes [7]- [9] or other convex sets [10]- [11].…”