This paper will study the exponential stable and state feedback stabilization of time delay singular systems with saturation actuators. Some sufficient conditions for existence of controller are obtained by using the linear matrix inequalities (LMIs) and integral inequality approach (IIA). When these LMIs are feasible, an explicit expression of controller is obtained. Based on Lyapunov–Krasovskii functional (LKF) techniques, a novel exponential stabilization criterion has been also derived in terms of LMIs which can be easily solved with efficient convex optimization algorithm. Our results are less conservative than some existing ones, and the decision variables involved in this paper are less than them. Examples illustrate our results as less conservative than those reported in the literature.
Issue Section:
Research Papers
References
1.
Dai
, L.
, 1989
, Singular Control Systems
, Springer-Verlag
, Berlin
.2.
Baser
, U.
, and Sahin
, U.
, 2011
, “Improved Delay-Dependent Robust Stabilization of Singular Systems
,” Int. J. Innovative Comput. Inf. Control
, 7
(1), pp. 177
–187
.3.
Boukas
, E. K.
, and Liu
, Z. K.
, 2003
, “Delay-Dependent Stability Analysis of Singular Linear Continuous-Time System
,” IEEE Proc. Control Theory Appl.
, 150
(4
), pp. 325
–330
.4.
Boukas
, E. K.
, and Al-Muthairi
, N. F.
, 2006
, “Delay-Dependent Stabilization of Singular Linear Systems With Delays
,” Int. J. Innovative Comput. Inf. Control
, 2
, pp. 283
–291
.5.
Feng
, Z. G.
, Lam
, J.
, and Gao
, H. J.
, 2011
, “Dissipativity Analysis of Singular Time-Delay Systems
,” Automatica
, 47
(11
), pp. 2548
–2552
.6.
Feng
, Z. G.
, and Lam
, J.
, 2015
, “On Reachable Set Estimation of Singular Systems
,” Automatica
, 52
, pp. 146
–153
.7.
Fridman
, E.
, 2001
, “A Lyapunov-Based Approach to Stability of Descriptor Systems With Delay
,” IEEE Conference on Decision and Control
(CDC
), Orlando, FL, Dec. 4–7, pp. 2850
–2855
.8.
Fridman
, E.
, 2002
, “Stability of Linear Descriptor Systems With Delay: A Lyapunov Based Approach
,” J. Math. Anal. Appl.
, 273
(1
), pp. 24
–44
.9.
Fridman
, E.
, and Shaked
, U.
, 2002
, “H∞-Control of Linear State-Delay Descriptor Systems: An LMI Approach
,” Linear Algebra Appl.
, 351–352
, pp. 271
–302
.10.
Gao
, H. L.
, Zhu
, S. Q.
, Chen
, Z. L.
, and Xu
, B. G.
, 2005
, “Delay-Dependent State Feedback Guaranteed Cost Control Uncertain Singular Time-Delay Systems
,” IEEE Conference on Decision and Control, and European Control Conference
(CDC-ECC
), Seville, Spain, Dec. 12–15, pp. 4354
–4359
.11.
Lewis
, F. L.
, 1986
, “A Survey of Linear Singular Systems
,” Circuits Syst. Signal Process.
, 5
(1
), pp. 3
–36
.12.
Li
, Z. X.
, Su
, H. Y.
, Gu
, Y.
, and Wu
, Z. G.
, 2013
, “Exponential Stability Analysis for Discrete-Time Singular Systems With Randomly Occurring Delay
,” Circuits Syst. Signal Process.
, 32
(5
), pp. 2231
–2242
.13.
Liu
, P.-L.
, 2012
, “Further Results on the Exponential Stability Criteria for Time Delay Singular Systems With Delay-Dependence
,” Int. J. Innovative Comput. Inf. Control
, 8
(6), pp. 4015
–4024
.http://www.ijicic.org/11-02079-1.pdf14.
Liu
, P.-L.
, 2013
, “Further Results on the Stability Analysis of Singular Systems With Time-Varying Delay: A Delay Decomposition Approach
,” Int. J. Anal.
, 2013
, p. 721407
.15.
Li
, J. K.
, 2010
, “Robust Guaranteed Cost Control for Singular Time-Delay Systems With Saturation Factors
,” Chinese Control and Decision Conference
(CCDC
), Xuzhou, China, May 26–28, pp. 340
–343
.16.
Su
, H. Y.
, Ji
, X. F.
, and Chu
, J.
, 2006
, “Delay-Dependent Robust Control for Uncertain Singular Time-Delay Systems
,” Asian J. Control
, 8
(2), pp. 180
–189
.17.
Zhang
, B. Y.
, Lam
, J.
, and Xu
, S. Y.
, 2015
, “Relaxed Results on Reachable Set Estimation of Time-Delay Systems With Bounded Peak Inputs
,” Int. J. Robust Nonlinear Control
, 26
(9), pp. 1994
–2007
.18.
Zhang
, B. Y.
, Lam
, J.
, and Xu
, S. Y.
, 2015
, “Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functional
,” IEEE Trans. Neural Networks Learn. Syst.
, 26
(7
), pp. 1480
–1492
.19.
Zhong
, R. X.
, and Yang
, Z.
, 2006
, “Delay-Dependent Robust Control of Descriptor Systems With Time Delay
,” Asian J. Control
, 8
(1), pp. 36
–44
.20.
Zhou
, S.
, Li
, Z.
, and Zhang
, C.
, 2010
, “Delay Decomposition Approach to Delay-Dependent Stability for Singular Time-Delay Systems
,” IET Control Theory Appl.
, 4
(11
), pp. 2613
–2620
.21.
Bernstein
, D. S.
, and Michel
, A. N.
, 1995
, “A Chronological Bibliography on Saturating Actuators
,” Int. J. Robust Nonlinear Control
, 5
(5
), pp. 375
–380
.22.
Liu
, P.-L.
, and Su
, T.-J.
, 1999
, “Stability Analysis of Uncertain Time-Delay Systems With Saturating Actuator
,” IEEE International Symposium on Industrial Electronics
(ISIE
), Bled, Slovenia, July 12–16, pp. 1076
–1081
.23.
Liu
, P.-L.
, 2005
, “Delay-Dependent Asymptotic Stabilization for Uncertain Time-Delay Systems With Saturating Actuators
,” Int. J. Appl. Math. Comput. Sci.
, 15
(1), pp. 45
–51
.http://zbc.uz.zgora.pl/Content/2580/Vol15No1-106.pdf24.
Liu
, P. L.
, 2011
, “Delay-Dependent Stabilization for Linear Time-Delay Uncertain Systems With Saturating Actuators
,” Int. J. Gen. Syst.
, 40
(3
), pp. 301
–312
.25.
Liu
, P. L.
, 2011
, “Exponential Delay Dependent Stabilization for Time-Varying Delay Systems With Saturating Actuator
,” ASME J. Dyn. Syst. Meas. Control
, 133
(1
), p. 014502
.26.
Manitius
, A. Z.
, 1984
, “Feedback Controllers for a Wind Tunnel Model Involving a Delay: Analytical Design and Numerical Simulation
,” IEEE Trans. Autom. Control
, 29
(12
), pp. 1058
–1068
.27.
Zhou
, B.
, Lin
, Z.
, and Duan
, G.
, 2010
, “Stabilization of Linear Systems With Input Delay and Saturation—A Parametric Lyapunov Equation Approach
,” Int. J. Robust Nonlinear Control
, 20
(13), pp. 1502
–1519
.28.
Zhou
, B.
, Lin
, Z.
, and Duan
, G. R.
, 2012
, “Truncated Predictor Feedback for Linear Systems With Long Time-Varying Input Delays
,” Automatica
, 48
(10
), pp. 2387
–2399
.29.
Lan
, W.
, and Huang
, J.
, 2003
, “Semiglobal Stabilization and Output Regulation of Singular Linear Systems With Input Saturation
,” IEEE Trans. Autom. Control
, 48
(7
), pp. 1274
–1280
.30.
Zhou
, W.-Z.
, Lu
, R.-Q.
, Su
, H.-Y.
, and Chu
, J.
, 2004
, “Robust Stabilization for Singular Systems With Time-Delays and Saturating Controls
,” American Control Conference
(ACC
), Boston, MA, June 30–July 2, pp. 4986
–4991
.http://ieeexplore.ieee.org/document/1384640/31.
Sun
, Y. J.
, 2003
, “Exponential Stability for Continuous-Time Singular Systems With Multiple Time Delays
,” ASME J. Dyn. Syst. Meas. Control
, 125
(2
), pp. 262
–264
.32.
Yue
, D.
, Lam
, J.
, and Ho
, D. W. C.
, 2005
, “Delay-Dependent Robust Exponential Stability of Uncertain Descriptor Systems With Time-Varying Delays
,” Dyn. Contin. Discrete Impulsive Syst. B
, 12
(1), pp. 129
–149
.http://hdl.handle.net/10722/15672833.
Boyd
, S.
, Ghaoui
, L. E.
, Feron
, E.
, and Balakrishnan
, V.
, 1994
, Linear Matrix Inequalities in System and Control Theory
, SIAM
, Philadelphia, PA
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