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Improved delay‐dependent stabilization of time‐delay systems with actuator saturation
Author(s) -
Dey Rajeeb,
Ghosh Sandip,
Ray Goshaidas,
Rakshit Anjan
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2925
Subject(s) - control theory (sociology) , nonlinear system , convex optimization , actuator , lyapunov function , term (time) , controller (irrigation) , mathematics , stability (learning theory) , representation (politics) , regular polygon , exponential stability , saturation (graph theory) , computer science , control (management) , law , physics , geometry , quantum mechanics , artificial intelligence , politics , combinatorics , machine learning , political science , agronomy , biology
SUMMARY This paper addresses the controller synthesis problem of linear time‐delay systems subjected to saturating control. Delay‐dependent regional stabilization criteria are derived based on Lyapunov–Krasovskii approach by using both the polytopic or dead‐zone representation of the saturation function. The main contribution of the paper lies in developing less conservative convex criterion in terms of LMIs to obtain superior results. On the basis of the derived stabilization criterion, an optimization problem is defined to compute the stabilizing state feedback gains with an aim to maximize the stabilizing region while guaranteeing the asymptotic stability of the closed‐loop system. Considering three numerical examples, an assessment of the polytopic and dead‐zone nonlinearity approaches is made. Copyright © 2012 John Wiley & Sons, Ltd.