\({\mathcal H}^\infty\) sensitivity minimization for delay systems
type: Item
instance of: scholarly article
title: \({\mathcal H}^\infty\) sensitivity minimization for delay systems
zbMATH Open document ID: 0627.93019
DOI: 10.1016/0167-6911(87)90004-1
author: David S. Flamm
author: Sanjoy K. Mitter
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: The paper announces results on the single input/single output \(H^{\infty}\) weighted sensitivity minimization control problem with transfer functions of the form \(P(s)=e^{-s\Delta}P_ 0(s)\), where \(P_ 0(s)\) is a minimum-phase and stable rational function, and \(\Delta >0\). The problem is to minimize \(\| W(s)(I+P(s)C(s))^{-1}\|\), where W(s) is the weighting function and C(s) ranges over all proper compensators for which the corresponding feedback system is internally stable. It is assumed that \(W(s)=(s+1)/(s+\beta)\), \(\beta >0\). Formulas for the infimal sensitivity are given, as well as the formulas for the optimal feedback compensator (when \(\beta <1)\). This compensator turns out to be an infinite dimensional system; approximation by rational proper feedback compensators is given.
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 4020938
zbMATH Keywords: H\({}^{\infty }\) weighted sensitivity minimization
zbMATH Keywords: infimal sensitivity
zbMATH Keywords: optimal feedback compensator
reviewed by: Leiba Rodman
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90004-1
OpenAlex ID: W2171551730
cites work: On decoupling the \(H^{\infty}\)-optimal sensitivity problem for products of plants
cites work: Weighted sensitivity minimization for delay systems
cites work: On H&lt;sup&gt;∞&lt;/sup&gt;-optimal sensitivity theory for SISO feedback systems
cites work: Q5521075
cites work: Q5727906
cites work: Generalized Interpolation in H ∞
cites work: Q3701889
cites work: An interpolation problem associated with \(H^{\infty}\)-optimal design in systems with distributed input lags
cites work: Q3802944
cites work: Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses
cites work: Feedback, minimax sensitivity, and optimal robustness
Recommended article: On the $H^\infty $-Optimal Sensitivity Problem for Systems with Delays
Recommended article: On the weighted sensitivity minimization problem for delay systems
Recommended article: On H&lt;sup&gt;∞&lt;/sup&gt;-optimal sensitivity theory for SISO feedback systems
Recommended article: ${\bf H}_\infty $ Optimal Sensitivity for a Class of Infinite-Dimensional Systems
Recommended article: Weighted sensitivity minimization for delay systems
Recommended article: Q4315505
Recommended article: \(L^ 1\) sensitivity minimization for plants with commensurate delays
Recommended article: Sensitivity Minimization by Strongly Stabilizing Controllers for a Class of Unstable Time-Delay Systems
Recommended article: Q3830884
Recommended article: Q3783895
description: scientific article; zbMATH DE number 4020938