This paper is concerned with the design of a robust, state-feedback, delay-dependent H controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.

References

References
1.
Soong
,
T. T.
, and
Constantinou
,
M. C.
, 1994,
Passive and Active Structure Vibration Control in Civil Engineering
,
Springer-Verlag
,
New York
.
2.
Guclu
,
R.
, and
Yazici
,
H.
, 2008, “
Vibration Control of a Structure With ATMD Against Earthquake Using Fuzzy Logic Controllers
,”
J. Sound Vib
,
318
(
1–2
), pp.
36
49
.
3.
Fujinami
,
T.
,
Saito
,
Y.
,
Morishita
,
M.
,
Koike
,
Y.
, and
Tanida
,
K.
, 2001, “
A Hybrid Mass Damper System Controlled by H Control Theory for Reducing Bending-Torsion Vibration of an Actual Building
,”
Earthquake Eng. Struct. Dyn.
,
30
, pp.
1639
1653
.
4.
Wang
,
S. G.
,
Yen
,
H. Y.
, and
Roschke
,
P. N.
, 2001, “
Robust H Control for Structural Systems With Parametric an Unstructured Uncertainties
,”
J. Vib. Control
,
7
, pp.
753
772
.
5.
Song
,
G.
,
Lin
,
J.
,
Zhao
,
Y.
,
Howson
,
P.
, and
Williams
,
W. F.
, 2007, “
Robust H Control for a Seismic Structures With Uncertainties in Model Parameters
,”
Earthquake Eng. Eng. Vib
,
6
(
4
), pp.
409
416
.
6.
Lim
,
C.
, 2008, “
Active Vibration Control of the Linear Structure With an Active Mass Damper Applying Robust Saturation Controller
,”
Mechatronics
,
18
, pp.
391
399
.
7.
Mahmoud
,
M. S.
, 2000,
Robust Control and Filtering for Time-Delay Systems
Marcel Dekker
,
New York
.
8.
Gu
,
K.
,
Kharitonov
,
V.
, and
Chen
,
J.
, 2003,
Stability of Time Delay Systems
,
Birkhauser
,
Basel
.
9.
Kucukdemiral
,
I. B.
, 2008, “
Delay-Dependent Guaranteed Cost Gain-Scheduling Control of LPV State-Delayed Systems
,”
Opt. Control Appl. Methods
,
29
, pp.
313
331
.
10.
Wu
,
M.
,
He
,
Y.
, and
She
,
J. H.
, 2010,
Stability Analysis and Robust Control of Time-Delay System
,
Springer
,
Beijing
.
11.
Parlakcı
,
M. N. A.
, 2006, “
Improved Robust Stability Criteria and Design of Robust Stabilizing Controller for Uncertain Linear Time-Delay Systems
,”
Int. J. Robust Nonlinear Control
,
16
, pp.
599
636
.
12.
Zhao
,
Y.
,
Gao
,
H.
,
Lam
,
J.
, and
Du
,
B.
, 2009, “
Stability and Stabilization of Delayed T-S Fuzzy Systems: A Delay Partitioning Approach
,”
IEEE Trans. Fuzzy Syst.
,
17
(
4
), pp.
750
762
.
13.
Parlakci
,
M. N. A.
, and
Kucukdemiral
,
I. B.
, 2010, “
Robust Delay-Dependent H Control of Time-Delay Systems With State and Input Delays
,”
Int. J. Robust Nonlinear Control
,
21
, pp.
974
1007
.
14.
Zhao
,
Y.
,
Zhang
,
C.
, and
Gao
,
H.
, 2009, “
A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties
,”
IEEE Trans. Syst. Man Cybern.
,
39
(
6
), pp.
1516
1527
.
15.
Agrawal
,
A. K.
, and
Yang
,
J. N.
, 1997, “
Effect of Fixed Time Delay on Stability and Performance of Actively Controlled Civil Engineering Structures
,”
Earthquake Eng. Struct. Dyn.
,
26
, pp.
1169
1185
.
16.
Du
,
H.
, and
Zhang
,
N.
, 2008, “
H Control for Buildings With Time Delay in Control via Linear Matrix Inequalities and Genetic Algorithms
,”
Eng. Struct.
,
30
, pp.
81
94
.
17.
Agrawal
,
A. K.
, and
Yang
,
J. N.
, 2000, “
Compensation of Time-Delay for Control Civil Engineering Structures
,”
Earthquake Eng. Struct. Dyn.
,
29
, pp.
37
62
.
18.
Cai
,
G. P.
,
Huang
,
J. Z.
, and
Yang
,
S. X.
, 2003, “
An Optimal Control Method for Linear System With Time Delay
,”
Comput. Struct.
,
81
, pp.
1539
1546
.
19.
Kose
,
I. E.
,
Schmitendorf
,
W.
,
Jabbari
,
F.
, and
Yang
,
J.
, 1996, “
H Active Seismic Response Control Using Static Output Feedback
,”
J. Eng. Mech.
,
122
(
7
), pp.
651
659
.
20.
Du
,
H.
,
Lam
,
J.
, and
Sze
,
K. Y.
, 2004, “
Non-Fragile H Vibration Control for Uncertain Structural Systems
,”
J. Sound Vib.
,
273
, pp.
1031
1045
.
21.
Agarwala
,
R.
,
Ozcelik
,
S.
, and
Faruqi
,
M.
, 2000, “
Active Vibration Control of a Multi-Degree-of-Freedom Structure by the Use of Direct Model Reference Adaptive Control
,”
American Control Conference
, Chicago, IL, pp.
3580
3584
.
22.
Aldemir
,
U.
, 2009, “
Causal Semi-Active Control of Seismic Response
,”
J. Sound Vib
,
322
, pp.
665
673
.
23.
Yagiz
,
N.
, 2001, “
Sliding Mode Control of a Multi-Degree-of-Freedom Structural System With Active Tuned Mass Damper
,”
Turk. J. Eng. Environ. Sci.
,
25
, pp.
651
657
.
24.
Guclu
,
R.
, and
Yazici
,
H.
, 2009, “
Self-Tuning Fuzzy Logic Control of a Non-Linear Structural System With ATMD Against Earthquake
,”
Nonlinear Dyn
,
56
(
3
), pp.
199
211
.
25.
Alli
,
H.
, and
Yakut
,
O.
, 2005, “
Fuzzy Sliding-Mode Control of Structures
,”
Eng. Struct.
,
27
, pp.
277
284
.
26.
Du
,
H.
, and
Zhang
,
N.
, 2008, “
Active Vibration Control of Structures Subject to Parametric Uncertainties and Actuator Delay
,”
J. Vib. Control
,
14
(
5
), pp.
689
709
.
27.
Ghaoui
,
L. E.
,
Qustry
,
F.
, and
Ait Rami
,
M.
, 1997, “
A Cone Complementarity Linearization Algorithm for Static Output-Feedback and Related Problems
,”
IEEE Trans. Autom. Control
,
42
(
8
), pp.
1171
1176
.
28.
Moon
,
Y. S.
,
Park
,
P.
,
Kwon
,
W. H.
, and
Lee
,
Y. S.
, 2001, “
Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems
,”
Int. J. Control
,
74
(
14
), pp.
1447
1455
.
29.
He
,
Y.
,
Wu
,
M.
,
She
,
J. H.
, and
Liu
,
G. P.
, 2004, “
Delay-Dependent Robust Stability Criteria for Uncertain Neutral Systems With Mixed Delays
,”
Syst. Control Lett.
,
51
(
1
), pp.
57
65
.
30.
He
,
Y.
,
Wang
,
Q. G.
,
Xie
,
L. H.
, and
Lin
,
C.
, 2007, “
Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay
,”
IEEE Trans. Autom. Control
,
52
(
2
), pp.
293
299
.
31.
Boyd
,
S.
,
Ghaoui
,
L. E.
,
Feron
,
E.
, and
Balakrishnan
,
V.
, 1994,
Linear Matrix Inequalities in System and Control Theory
,
Society for Industrial and Applied Mathematics (SIAM)
,
Philadelphia
, pp.
7
8
.
32.
Löfberg
,
J.
, 2004, “
Yalmip: A Toolbox for Modeling and Optimization in matlab
,”
Proceedings of the CACSD Conference
, Taipei, Taiwan.
33.
Strum
,
J. F.
1999, “
Using SeDuMi 1.02 a matlab for Optimization Over Symmetric Cones
,”
Optim. Methods Software
,
11
(
2
), pp.
625
653
.
34.
Guclu
,
R.
, and
Yazici
,
H.
, 2009, “
Self-Tuning Fuzzy Logic Control of a Non-Linear Structural System With ATMD Against Earthquake
,”
Nonlinear Dyn.
,
56
(
3
), pp.
199
211
.
35.
Guclu
,
R.
, and
Yazici
,
H.
, 2007, “
Fuzzy-Logic Control of Non-Linear Structural System Against Earthquake Induced Vibration
,”
J. Vib. Control
,
13
(
11
), pp.
1535
1551
.
36.
Guclu
,
R.
, 2003, “
Fuzzy Logic Control of Vibrations of Analytical Multi-Degree-of-Freedom Structural Systems
,”
Turk. J. Eng. Environ. Sci.
,
27
, pp.
157
168
.
37.
Yagiz
,
N.
, 2003, “
Vibration Control of a Building With ATMD Under Earthquake Excitation
,”
Int. J. Appl. Mech. Eng.
,
8
(
1
), pp.
117
123
.
38.
Yagiz
,
N.
, and
Ertal
,
C.
, 2003, “
Evaluation of Control Methods on a Structural System
,”
Math. Comput. Appl.
,
8
(
3
), pp.
369
376
.
39.
Kasimzade
,
A. A.
, 2004,
Structural Dynamics
,
Birsen Publication
,
Istanbul, Turkey.
40.
Yoshida
,
O.
, and
Dyke
,
S. J.
, 2004, “
Seismic Control of a Nonlinear Benchmark Building Using Smart Dampers
,”
J. Eng. Mech.
,
130
(
4
), pp.
386
392
.
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