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Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization
Joint Authors
Castelan, Eugênio B.
Klug, Michael
Silva, Luís F. P.
Leite, Valter J. S.
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-20
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
A convex condition in terms of linear matrix inequalities (LMIs) is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays.
A Takagi-Sugeno (T-S) fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity.
The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K) function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity.
This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions.
Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model.
Numerical simulations are given to illustrate this proposal.
American Psychological Association (APA)
Silva, Luís F. P.& Leite, Valter J. S.& Castelan, Eugênio B.& Klug, Michael. 2014. Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-483054
Modern Language Association (MLA)
Silva, Luís F. P.…[et al.]. Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization. Mathematical Problems in Engineering No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-483054
American Medical Association (AMA)
Silva, Luís F. P.& Leite, Valter J. S.& Castelan, Eugênio B.& Klug, Michael. Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-483054
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483054