Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure

An improvement of QFT plant template generation for systems with affinely dependent parametric uncertainties

“…Theorem 2 (Kogan and Leizarowitz [19] and Polyak and Kogan [20]). If a complex point z lies on the boundary of the value set hðBÞ, i.e., z 2 @hðBÞ, then every q 2 B such that z ¼ hðqÞ is a principal point.…”

“…Therefore, in order to reduce the computational burden for generating the plant template boundary @Gðjo; BÞ, it is desired to develop an efficient method to identify the set of points lying on the edges of the box B whose image does not contribute to the boundary of the plant template Gðjo; BÞ. To this end, the principal point notion introduced by Kogan and Leizarowitz [19] and Polyak and Kogan [20] is used. A point q 2 B is a principal point associated with a mapping h : B !…”

A New Approach to Mixed H2/H∞ Optimal PI/PID Controller Design

“…In the following, we apply the notion of principal points [29][30][31] to characterize the boundary of the H ∞ constraint set E(k d ,γ), i.e., to characterize ∂E(k d ,γ).…”

Parameter Stability Margins for Polynomial Uncertainty Structures: A Polynomial Programming Approach

“…However, in many engineering applications, the coefficients often turn out to be multilinear, polynomial or nonlinear functions of the system's uncertain parameters (Bhattacharyya, et al, 1995;Ackermann, 2002), and in these cases, the research has been less fruitful. Several representative contributions in these problem areas, mainly in the stability analysis context, are given in (Chapellat, et al, 1993;Djaferis, 1995;Polyak and J. Kogan, 1995;Zettler and Garloff, 1998).…”

“…Thus, multilinear results can be obtained in these cases. For the case of multilinear dependency, the well-known Mapping Theorem (Zadeh and Desoer, 1963) is one of the few tools available for checking robust stability; however, it is recognized that the sufficiency conditions of this theorem can lead to conservative results (Polyak and Kogan, 1995). The Mapping Theorem is used in (Sideris and Sánchez Peña, 1989;Sideris and Sánchez Peña, 1989;De Gaston and Safonov, 1988;Keel and Bhattacharyya, 1993) to develop several algorithms for determining lower bounds for stability margins for the multilinear case.…”