Premium
Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems
Author(s) -
Parlakçı M. N. Alpaslan
Publication year - 2006
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.1086
Subject(s) - control theory (sociology) , mathematics , linear matrix inequality , norm (philosophy) , weighting , robust control , convex optimization , bounded function , stability theory , stability (learning theory) , upper and lower bounds , mathematical optimization , regular polygon , computer science , control system , control (management) , nonlinear system , engineering , artificial intelligence , law , mathematical analysis , geometry , quantum mechanics , machine learning , political science , radiology , medicine , physics , electrical engineering
In this paper, an improved linear matrix inequality (LMI)‐based robust delay‐dependent stability test is introduced to ensure a larger upper bound for time‐varying delays affecting the state vector of an uncertain continuous‐time system with norm‐bounded‐type uncertainties. A quasi‐full‐size Lyapunov–Krasovskii functional is chosen and free‐weighting matrix approach is employed. Less restrictive sufficient conditions are derived for robust stability of time‐varying delay systems with norm‐bounded‐type uncertainties. Moreover, the investigation of the stabilization problem with memoryless state‐feedback control is presented such that the stabilizability criteria are obtained in terms of matrix inequalities, which can be solved via utilizing a cone complementarity minimization algorithm. Finally, the problem of output feedback stabilization for square systems is also taken into consideration. The output feedback stabilizability criteria are derived in the form of linear matrix inequalities, which are convex and can be easily solved using interior point algorithms. A plenty of numerical examples are presented indicating that the proposed stability and stabilization methods effectively improve the existing results. Copyright © 2006 John Wiley & Sons, Ltd.