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Robust Stability and Stabilization of Positive Interval Systems Subject to Actuator Saturation
Author(s) -
Zhang JiShi,
Deng Zeguan,
Wang YanWu
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.833
Subject(s) - control theory (sociology) , convex optimization , lyapunov function , mathematics , linear matrix inequality , stability theory , domain (mathematical analysis) , actuator , interval (graph theory) , stability (learning theory) , linear system , regular polygon , mathematical optimization , computer science , control (management) , nonlinear system , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , combinatorics , machine learning
This paper addresses the stabilization problem for a class of uncertain positive linear systems ( PLSs ) in the presence of saturating actuators. The objective is to obtain sufficient conditions for the robust stability of PLSs and to design robust state feedback control laws such that the closed‐loop uncertain system is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for robust stabilization and positivity are derived via the Lyapunov function approach and convex analysis method for both the discrete‐time and the continuous‐time cases, respectively. The state feedback controller design and the estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities ( LMIs ) constraints. A numerical example is given to show the effectiveness of the proposed methods.