A control problem of Takagi–Sugeno fuzzy systems with a time-varying input delay and norm-bounded uncertainties is addressed. The input delay is well-known in making the closed-loop stabilization difficult. A sufficient condition for the robust fuzzy-model-based stabilization is derived based on the Lyapunov–Razumikhin stability theorem, without the assumption of the variation rate on the delay. A constructive design scheme is presented in the form of the iterative convex optimization problem. The effectiveness of the proposed method is demonstrated by a numerical simulation of a nonlinear mass-spring-damper system.
Issue Section:
Technical Briefs
1.
He
, J. B.
, Wang
, Q. G.
, and Lee
, T. H.
, 2000, “PI/PID Controller Tuning Via LQR Approach
,” Chem. Eng. Sci.
0009-2509, 55
, pp. 2429
–2439
.2.
Roh
, Y. H.
, and Oh
, J. H.
, 2000, “Sliding Mode Control With Uncertainty Adaptation for Uncertain Input-Delay Systems
,” Int. J. Control
0020-7179, 73
(13
), pp. 1255
–1260
.3.
Overstreet
, J. W.
, and Tzes
, A.
, 1999, “An Internet-Based Real-Time Control Engineering Laboratory
,” IEEE Control Syst. Mag.
0272-1708, 195
, pp. 19
–34
.4.
Kolmanovskii
, V. B.
, Niculescu
, S. I.
, and Richard
, J. R.
, 1999, “On the Liapunov–Krasovskii functionals for stability analysis of linear delay systems
,” Int. J. Control
0020-7179, 72
(4
), pp. 374
–384
.5.
Inamdar
, S. R.
, Kumar
, V. R.
, and Kulkarni
, B. D.
, 1991, “Dynamics of Reacting Systems in the Presence of Time-Delay
,” Chem. Eng. Sci.
0009-2509, 46
(3
), pp. 901
–908
.6.
Moon
, Y. S.
, Park
, P. G.
, and Kwon
, W. H.
, 2001, “Robust Stabilization of Uncertain Input-Delayed Systems Using Reduction Method
,” Automatica
0005-1098, 37
, pp. 307
–312
.7.
Hale
, J. K.
, 1977, Theory of Functional Differential Equations
, Springer-Verlag
, New York.8.
Tanaka
, K.
, Ikeda
, T.
, and Wang
, H. O.
, 1998, “Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-Based Designs
,” IEEE Trans. Fuzzy Syst.
1063-6706, 6
(2
), pp. 250
–265
.9.
Lee
, H. J.
, Park
, J. B.
, and Chen
, G.
, 2001, “Robust Fuzzy Control of Nonlinear Systems With Parametric Uncertainties
,” IEEE Trans. Fuzzy Syst.
1063-6706, 9
(2
), pp. 369
–379
.10.
Joo
, Y. H.
, Chen
, G.
, and Shieh
, L. S.
, 1999, “Hybrid State-Space Fuzzy Model-Based Controller With Dual-Rate Sampling for Digital Control of Chaotic Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 7
(4
), pp. 394
–408
.11.
Chang
, W.
, Park
, J. B.
, Joo
, Y. H.
, and Chen
, G.
, 2002, “Design of Robust Fuzzy-Model-Based Controller With Sliding Mode Control for SISO Nonlinear Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 125
(1
), pp. 1
–22
.12.
Chang
, W.
, Park
, J. B.
, Joo
, Y. H.
, and Chen
, G.
, 2002, “Design of Sampled-Data Fuzzy-Model-Based Control Systems by Using Intelligent Digital Redesign
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
1057-7122, 49
(4
), pp. 509
–517
.13.
Lee
, K. R.
, Kim
, J. H.
, Jeung
, E. T.
, and Park
, H. B.
, 2000, “Output Feedback Robust H∞ Control of Uncertain Fuzzy Dynamic Systems With Time-Varying Delay
,” IEEE Trans. Fuzzy Syst.
1063-6706, 8
(6
), pp. 657
–665
.14.
Cao
, Y. Y.
, and Frank
, P. M.
, 2000, “Analysis and Synthesis of Nonlinear Time-Delay Systems Via Fuzzy Control Approach
,” IEEE Trans. Fuzzy Syst.
1063-6706, 8
(2
), pp. 200
–211
.Copyright © 2005
by American Society of Mechanical Engineers
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