Showing papers by "Ian R. Petersen published in 1989"
TL;DR: In this paper, the problem of determining if all polynomials in a family have the property that all of their roots lie within a given region is discussed, and a notion of a Kharitonov region is defined.
Abstract: Families of complex polynomials whose coefficients lie within given intervals are discussed. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie within a given region is discussed. Towards this end, a notion of a Kharitonov region is defined. Roughly speaking, a Kharitonov region is a region in the complex plane with the following property: given any suitable family of polynomials, in order to determine if all polynomials in the family have all of their roots in the region, it suffices to check only the vertex polynomials of the family. The main result is a sufficient condition for a given region to be a Kharitonov region. >
61 citations
TL;DR: In this article, the authors considered a problem of disturbance attenuation using full state feedback and gave a complete solution to this problem in terms of a certain algebraic Riccati equation.
Abstract: The author considers a problem of disturbance attenuation using full state feedback. The particular class of linear systems under consideration is closely related to the one-block problem in H/sup infinity / control. The author gives a complete solution to this problem in terms of a certain algebraic Riccati equation. >
29 citations
01 Jan 1989
TL;DR: In this paper, the stability of families of polynomials has been studied in the context of control systems with uncertain parameters, where the set of allowable uncertain parameters is mapped to the polynomial coefficients.
Abstract: In 1978, a significant new result on the stability of families of polynomials was published by V.L. Kharitonov in Russian [1]. When this result became known in the Western literature, there followed an explosion of results related to Kharitonov’s Theorem; e.g., see [2]–[15]. One of the reasons for the large amount of interest generated by these results is the fact that they provide powerful tools in the design and analysis of control systems which are robust against parameter uncertainty; e.g., see [15]. Indeed, the family of polynomials under consideration is typically the set of all possible characteristic polynomials for a control system containing uncertain parameters. This family of polynomials is generated by mapping the set of allowable uncertain parameters into the set of allowable polynomials coefficients.
2 citations
03 Apr 1989