This paper addresses a new approach on and passivity control via static and integral output feedback controllers of continuous-time linear systems with input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback /passivity stabilizability are proposed for the closed-loop system in terms of matrix inequalities. These new characterizations possess a special monotonic property, which underpin the convergence of a linearized iterative computational algorithm. The effectiveness and merits of the proposed approach are illustrated through numerical examples.
Issue Section:
Research Papers
References
1.
Dong
, H.
, Wang
, Z.
, and Gao
, H.
, 2009, “Robust H∞ Filtering of Nonlinear Networked Systems With Multiple Stochastic Communication Delays
,” Proceedings of the 7th Asian Control Conference, pp. 203
–208
.2.
He
, Y.
, Wu
, M.
, She
, J.
, and Liu
, G.
, 2004, “Parameter-Dependent Lyapunov Functional for Stability of Time-Delay Systems With Polytopic-Type Uncertainties
,” Automatica
, 49
(5
), pp. 828
–832
.3.
Niculescu
, S.-I.
, and Lozano
, R.
, 2001 “On the Passivity of Linear Delay Systems
,” IEEE Trans. Autom. Control
, 46
(3
), pp. 460
–464
.4.
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
.5.
Chen
, J.-D.
, 2007, “Delay-Dependent Robust H∞ Control of Uncertain Neutral Systems With State and Input Delays: LMI Optimization Approach
,” Chaos
, Solitons Fractals, 33
, pp. 595
–606
.6.
Dong
, H.
, Wang
, Z.
, Ho
, D. W. C.
, and Gao
, H.
, 2010, “Robust H∞ Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements
,” IEEE Trans. Fuzzy Syst.
, 18
(4
), pp. 712
–725
.7.
Lam
, J.
, Gao
, H.
, and Wang
, C.
, 2005, “Model Reduction of Linear System With Distributed Delay
,” IEE Proc.: Control Theory Appl.
, 152
(6
), pp. 662
–674
.8.
Suplin
, V.
, Fridman
, E.
, and Shaked
, U.
, 2006, “H∞ Control of Linear Uncertain Time-Delay Systems—A Projection Approach
,” IEEE Trans. Autom. Control
, 51
(4
), pp. 680
–685
.9.
Park
, J.
, 2004, “Designing a Dynamic Output Feedback Controller for a Class of Neutral systems With Discrete and Distributed Delays
,” IEE Proc.: Control Theory Appl.
, 151
(5
), pp. 610
–614
.10.
Fridman
, E.
, and Shaked
, U.
, 2002, “A Descriptor System Approach to H∞ Control of Time-Delay Systems
,” IEEE Trans. Autom. Control
, 47
(2
), pp. 253
–270
.11.
Shu
, Z.
, and Lam
, J.
, 2009, “An Augmented System Approach to Static Output-Feedback Stabilization With H∞ Performance for Continuous-Time Plants
,” Int. J. Robust Nonlinear Control
, 19
, pp. 768
–785
.12.
Fridman
, E.
, and Shaked
, U.
, 2003, “Parameter Dependent Stability and Stabilization of Uncertain Time-Delay Systems
,” IEEE Trans. Autom. Control
, 48
(5
), pp. 861
–866
.13.
He
, Y.
, Wang
, Q.
, Xie
, L.
, 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
.14.
He
, Y.
, Wu
, M.
, Lie
, G.
, and Hua
, J.
, 2008, “Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay
,” IEEE Trans. Autom. Control
, 53
(10
), pp. 2372
–2377
.15.
Wu
, M.
, He
, Y.
, She
, J.
, and Liu
, G.
, 2004, “Delay-Dependent Criteria for Robust Stability of Time-Varying Delay Systems
,” Automatica
, 40
, pp. 1435
–1439
.16.
Lu
, G. P.
, Yeung
, L. F.
, Ho
, D. W. C.
, and Zheng
, Y.
, 2000, “Strict Positive Realness for Linear Time-Invariant Systems With Time-Delays
,” IEEE Conference on Decision and Control, pp. 5004
–5009
.17.
Fridman
, E.
, and Shaked
, U.
, 2002, “On Delay-Dependent Passivity
,” IEEE Trans. Autom. Control
, 47
(4
), pp. 664
–669
.18.
Xu
, S.
, and Lam
, J.
, 2008, “A Survey of Linear Matrix Inequality Techniques in Stability Analysis of Delay Systems
,” Int. J. Syst. Sci.
, 39
(12
), pp. 1095
–1113
.19.
R.
Lozano
, B.
Brogliato
, O. E.
, and Maschke
, B.
, 2000, Dissipative Systems Analysis and Control Theory and Applications
, Springer-Verlag
, London, United Kingdom
.20.
Du
, B.
, Lam
, J.
, Shu
, Z.
, and Wang
, Z.
, 2009, “A Delay-Partitioning Projection Approach to Stability Analysis of Continuous Systems With Multiple Delay Components
,” IEE Proc.: Control Theory Appl.
, 3
(4
), pp. 383
–390
.21.
Gu
, K.
, Kharitonov
, V.
, and Chen
, J.
, 2003, Stability of Time-Delay Systems, Birkhauser, Boston
, MA.22.
Du
, B.
, Lam
, J.
, and Shu
, Z.
, 2010, “Stabilization for Input Delay systems via Static and Integral Output Feedback
,” Automatica
, 46
, pp. 2000
–2007
.23.
Fridman
, E.
, Shaked
, U.
, and Suplin
, V.
, 2005, “Input/Output Delay Approach to Robust Sampled-Data H∞ Control
,” Syst. Control Lett.
, 54
(3
), pp. 271
–282
.24.
Zhang
, X.
, Wu
, M.
, She
, J.
, and He
, Y.
, 2005, “Delay-Dependent Stabilization of Linear Systems With Time-Varying State and Input Delays
,” Automatica
, 41
(8
), pp. 1405
–1412
.25.
Witrant
, E.
, de Wit
, C. C.
, Georges
, D.
, and Alamir
, M.
, 2004, “Remote Stabilization via Time-Varying Communication Network Delays: Application to TCP networks
,” IEEE Conference on Control Applications, pp. 474
–479
.26.
Chiasson
, J.
, 2007, Applications of Time Delay Systems
, Springer-Verlag
, London, United Kingdom
.27.
Niculescu
, S.-I.
, Gu
, K.
, and Abdallah
, C.
, 2003, “Some Remarks on the Delay Stabilizing Effect in SISO Systems
,” Proceedings of American Control Conference, pp. 2670
–2675
.28.
Seuret
, A.
, Edwards
, C.
, Spurgeon
, S. K.
, and Fridman
, E.
, 2009, “Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay
,” IEEE Trans. Autom. Control
, 54
(2
), pp. 256
–265
.29.
Chen
, W.
, and Zheng
, W.
, 2006, “On Improved Robust Stabilization of Uncertain Systems With Unknown Input Delay
,” Automatica
, 42
, pp. 1067
–1072
.30.
Başer
, U.
, and Kizilsac
, B.
, 2007, “Dynamic Output Feedback H∞ Control Problem for Linear Neutral Systems
,” IEEE Trans. Autom. Control
, 52
(6
), pp. 1113
–1118
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