Stabilization of time-varying system by controllers with internal loop
type: Item
instance of: scholarly article
title: Stabilization of time-varying system by controllers with internal loop
zbMATH Open document ID: 1264.70016
DOI: 10.1155/2012/132597
author: Chengkai Shi
author: Yufeng Lu
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We study the concept of stabilization with internal loop for infinite-dimensional discrete time-varying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the controller with internal loop overcomes the awkwardness brought by the extra invertibility condition in the parametrization of the conventional controllers. We also prove that the strong stabilization problem can be completely solved in the closed-loop system with internal loop. Thus the advantage of the controller with internal loop is addressed in the framework of nest algebra.
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70E50
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70K45
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 6173044
Wikidata QID: Q58912462
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/132597
OpenAlex ID: W1985594506
cites work: Dynamic stabilization of regular linear systems
cites work: Coprime factorization for regular linear systems
cites work: Optimizability and estimatability for infinite-dimensional linear systems
cites work: Coprime Factorization and Dynamic Stabilization of Transfer Functions
cites work: Q4534552
cites work: Q3590789
cites work: Robust control theory in Hilbert space
cites work: A game theory approach to mixed control for a class of stochastic time-varying systems with randomly occurring nonlinearities
cites work: Probability-guaranteed \(H_\infty\) finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations
cites work: Error-constrained finite-horizon tracking control with incomplete measurements and bounded noises
cites work: H ∞ filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts
cites work: Error-Constrained Filtering for a Class of Nonlinear Time-Varying Delay Systems With Non-Gaussian Noises
cites work: Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations
cites work: Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case
cites work: On strong stabilization for linear time-varying systems
description: scientific article; zbMATH DE number 6173044