Finite-time \(l_1\)-gain control for positive switched systems with time-varying delay via delta operator approach
type: Item
instance of: scholarly article
title: Finite-time \(l_1\)-gain control for positive switched systems with time-varying delay via delta operator approach
zbMATH Open document ID: 1406.93147
DOI: 10.1155/2014/872158
author: Shuo Li
author: Zhengrong Xiang
author: Hamid Reza Karimi
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper is concerned with the problem of finite-time \(l_1\)-gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee the \(l_1\)-gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with an \(l_1\)-gain performance. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the proposed method.
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 7023233
zbMATH Keywords: time-varying delay
zbMATH Keywords: finite-time \(l_1\)-gain control
zbMATH Keywords: positive switched systems
zbMATH Keywords: state feedback controller
zbMATH Keywords: finite-time stability
Wikidata QID: Q59042206
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/872158
OpenAlex ID: W2093739204
cites work: Positive 1D and 2D systems
cites work: Constrained Control of Positive Systems with Delays
cites work: Analysis and design of AIMD congestion control algorithms in communication networks
cites work: A positive linear discrete-time model of capacity planning and its controllability properties
cites work: Coordination of groups of mobile autonomous agents using nearest neighbor rules
cites work: The Choice of the Forms of Lyapunov Functions for a Positive 2D Roesser Model
cites work: Q5439865
cites work: Linear Copositive Lyapunov Functions for Continuous-Time Positive Switched Systems
cites work: On the Stability of Switched Positive Linear Systems
cites work: Stability of switched positive linear systems with average dwell time switching
cites work: Rapprochement between continuous and discrete model reference adaptive control
cites work: Q3990551
cites work: Improved finite word length characteristics in digital control using delta operators
cites work: The zeros and poles of delta operator systems
cites work: Properties of the delta operator model of dynamic physical systems
cites work: Stability analysis and stabilization of T-S fuzzy delta operator systems with time-varying delay via an input-output approach
cites work: Stability of a class of switched positive linear time‐delay systems
cites work: Stability Analysis of Positive Switched Linear Systems With Delays
cites work: \(H_\infty\) finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance
cites work: Q5555195
cites work: Stability of discrete systems over a finite interval of time†
cites work: Robust finite-time \(H_{\infty }\) control for a class of uncertain switched neutral systems
cites work: Finite-time boundedness and \(L_{2}\)-gain analysis for switched delay systems with norm-bounded disturbance
cites work: Finite-time stability of switched positive linear systems
cites work: Finite-time \(L_1\) control for positive switched linear systems with time-varying delay
cites work: Stability, \(L_1\)-gain and control synthesis for positive switched systems with time-varying delay
cites work: Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach
description: scientific article; zbMATH DE number 7023233