Delay-dependent finite-time \(H_{\infty}\) controller design for a kind of nonlinear descriptor systems via a T-S fuzzy model
type: Item
instance of: scholarly article
title: Delay-dependent finite-time \(H_{\infty}\) controller design for a kind of nonlinear descriptor systems via a T-S fuzzy model
zbMATH Open document ID: 1394.93170
DOI: 10.1155/2015/546835
author: Baoyan Zhu
author: Jingjun Zhang
author: Daqing Zhang
author: Aibin Liu
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Delay-dependent finite-time \(H_{\infty}\) controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time \(H_{\infty}\) controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the \(H_{\infty}\) performance to a prescribed disturbance attenuation level \(\gamma\). The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a \(H_{\infty}\) performance level.
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 6926624
Wikidata QID: Q59119260
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/546835
OpenAlex ID: W1847986717
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description: scientific article; zbMATH DE number 6926624