Frequency conditions in \(H^\infty\)-control and absolute stabilization problems
type: Item
instance of: scholarly article
title: Frequency conditions in \(H^\infty\)-control and absolute stabilization problems
zbMATH Open document ID: 0892.93029
author: V. A. Brusin
published in: Doklady Mathematics
publication date: 1998-02-05T00:00:00Z
review text: It is known that solving Lur'e-Riccati matrix equations in the theory of absolute stability is connected with the existence of a special solution of variational problems with an integral quadratic functional. Frequency inequalities that arise in this theory are existence conditions of solutions to these variational problems. Riccati matrix equations of a special form also arise in investigations on \(H^\infty\)-control. This class of Riccati equations is connected with a minimax problem, and their solution is connected with the presence of a saddle point in the function space in which the minimax problem is embedded. In turn, \(H^\infty\)-control problems intersect with nonlinear absolute stabilization problems. In this paper, the author establishes the frequency inequalities that are existence conditions of solutions for the considered class of \(H^\infty\)-control and absolute stabilization problems.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93D10
Mathematics Subject Classification ID: 93C80
zbMATH DE Number: 1099478
zbMATH Keywords: \(H^\infty\)-control
zbMATH Keywords: frequency response methods
zbMATH Keywords: Popov-type stability of feedback systems
zbMATH Keywords: frequency inequalities
zbMATH Keywords: existence conditions
zbMATH Keywords: absolute stabilization problems
zbMATH Keywords: Riccati matrix equations
zbMATH Keywords: minimax problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1099478