This paper studies the problem of designing insensitive output-feedback controllers for linear discrete-time systems. The designed controllers are insensitive to additive/multiplicative controller coefficient variations. An LMI-based procedure, which is a sequential linear programming matrix method (SLPMM), is proposed to solve the considered problem which is a nonconvex problem itself. It is worth mentioning that the nonfragile control design method is adopted to obtain an effective solution for accelerating convergence of SLPMM algorithm due to the fact that a good starting point for the iteration is very important.
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Technical Briefs
References
1.
Whidborne
, J. F.
, Istepanian
, R. S. H.
, and Wu
, J.
, 2001
, “Reduction of Controller Fragility by Pole Sensitivity Minimization
,” IEEE Trans. Autom. Control
, 46
(2
), pp. 320
–325
.10.1109/9.9057022.
Yamaki
, S.
, Abe
, M.
, and Kawamata
, M.
, 2008
, “On the Absence of Limit Cycles in State-Space Digital Filters With Minimum L2-Sensitivity
,” IEEE Trans. Circuits Syst. Express Briefs
, 55
(1
), pp. 46
–50
.10.1109/TCSII.2007.9077573.
Li
, G.
, 1998
, “On the Structure of Digital Controllers With Finite Word Length Consideration
,” IEEE Trans. Autom. Control
, 43
(5
), pp. 689
–693
.10.1109/9.7288724.
Guo
, X. G.
, and Yang
, G. H.
, 2011
, “H∞ Filter Design for Delta Operator Formulated Systems With Low Sensitivity to Filter Coefficient Variations
,” IET Control Theory Appl.
, 5
(15
), pp. 1677
–1688
.10.1049/iet-cta.2010.05005.
Che
, W. W.
, and Yang
, G. H.
, 2011
, “Non-Fragile Dynamic Output Feedback H∞ Control for Discrete-Time Systems
,” Int. J. Control Autom. Syst.
, 9
(5
), pp. 993
–997
.10.1007/s12555-011-0522-76.
Che
, W. W.
, and Wang
, Y. L.
, 2011
, “Non-Fragile Dynamic Output Feedback H∞ Control for Continuous-Time Systems With Controller Coefficient Sensitivity Consideration
,” Proceedings of 2011 Chinese Control Decision and Conference
, Mianyang, China, pp. 2441
–2446
.7.
Ding
, D. W.
, Li
, X. L.
, Yin
, Y. X.
, and Sun
, C. G.
, 2012
, “Non-Fragile H∞ and H2 Filter Designs for Continuous-Time Linear Systems Based on Randomized Algorithms
,” IEEE Trans. Ind. Electron.
, 59
(11
), pp. 4433
–4442
.10.1109/TIE.2011.21593508.
Leibfritz
, F.
, 2000
, “An LMI-Based Algorithm for Designing Suboptimal Static H2
/H∞ Output Feedback Controllers
,” SIAM J. Control Optim.
, 39
(6
), pp. 1711
–1735
.10.1137/S03630129993495539.
Li
, L.
, and Jia
, Y.
, 2009
, “Non-Fragile Dynamic Output Feedback Control for Linear Systems With Time-Varying Delay
,” IET Control Theory Appl.
, 3
(8
), pp. 995
–1005.10.1049/iet-cta.2008.000810.
Zhu
, G.
, Grigoriadis
, K. M.
, and Skelton
, R. E.
, 1994
, “Optimal Finite Wordlength Digital Control With Skewed Sampling,” Proceeding of 1994 American Control Conference
, Baltimore, MD, 3, pp. 3482–3486.10.1109/ACC.1994.73522611.
de Oliveira
, M. C.
, Bemussou
, J.
, and Geromel
, J. C.
, 2002
, “Extended H2 and H∞ Norm Characterizations and Controller Parametrizations for Discrete-Time Systems
,” Int. J. Control
, 75
(9
), pp. 666
–679
.10.1080/0020717021014021212.
Löfberg
, J.
, 2004
, “YALMIP: A Toolbox for Modeling and Optimization in MATLAB
,” Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design
, Taipei, Taiwan, China, pp. 284
–289
.13.
Labit
, Y.
, Peaucelle
, D.
, and Henrion
, D.
, 2002
, “SeDumi interface 1.02: A Tool for Solving LMI Problems With SeDumi
,” Proceedigns of 2002 International Symposium on Computer Aided Control System Design
, Toulouse, France, pp. 272
–277
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