This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system.
Issue Section:
Research Papers
References
1.
Bako
, L.
, 2011
, “Identification of Switched Linear Systems Via Sparse Optimization
,” Automatica
, 47
(4
), pp. 668
–677
.2.
Bejarano
, F. J.
, and Pisano
, A.
, 2011
, “Switched Observers for Switched Linear Systems With Unknown Inputs
,” IEEE Trans. Autom. Control
, 56
(3
), pp. 681
–686
.3.
Koenig
, D.
, Marx
, B.
, and Jacquet
, D.
, 2008
, “Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems
,” IEEE Trans. Autom. Control
, 53
(1
), pp. 373
–379
.4.
Ríos
, H.
, Davila
, J.
, and Fridman
, L.
, 2012
, “High-Order Sliding Mode Observers for Nonlinear Autonomous Switched Systems With Unknown Inputs
,” J. Franklin Inst.
, 349
(10
), pp. 2975
–3002
.5.
Hernandez
, S. M.
, and García
, R. A.
, 2014
, “An Observer for Switched Lipschitz Continuous Systems
,” Int. J. Control
, 87
(1
), pp. 207
–222
.6.
Lin
, H.
, and Antsaklis
, P. J.
, 2009
, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
,” IEEE Trans. Autom. Control
, 54
(2
), pp. 308
–322
.7.
Wang
, X.
, and Shao
, C.
, 2013
, “Finite-Time Input-to-State Stability and Optimization of Switched Nonlinear Systems
,” ASME J. Dyn. Syst. Meas. Control
, 135
(4
), p. 041018
.8.
Jasim
, N. F.
, 2013
, “Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems
,” ASME J. Dyn. Syst. Meas. Control
, 135
(5
), p. 051011
.9.
Sun
, Z.
, 2006
, “Stabilization and Optimization of Switched Linear Systems
,” Automatica
, 42
(5
), pp. 783
–788
.10.
Zhao
, X.
, Liu
, X.
, Yin
, S.
, and Li
, H.
, 2014
, “Improved Results on Stability of Continuous-Time Switched Positive Linear Systems
,” Automatica
, 50
(2
), pp. 614
–621
.11.
Zhao
, X.
, Li
, H.
, and Niu
, B.
, 2015
, “Switching Stabilization for a Class of Slowly Switched Systems
,” IEEE Trans. Autom. Control
, 60
(1
), pp. 221
–226
.12.
Deaecto
, G. S.
, Daafouz
, J.
, and Geromel
, J. C.
, 2012
, “H2 and H∞ Performance Optimization of Singularly Perturbed Switched Systems
,” SIAM J. Control Optim.
, 50
(3
), pp. 1597
–1615
.13.
Chatterjee
, D.
, and Liberzon
, D.
, 2011
, “Stabilizing Randomly Switched Systems
,” SIAM J. Control Optim.
, 49
(5
), pp. 2008
–2031
.14.
Zhou
, L.
, Ho
, D. W. C.
, and Zhai
, G.
, 2013
, “Stability Analysis of Switched Linear Singular Systems
,” Automatica
, 49
(5
), pp. 1481
–1487
.15.
Chen
, Y.
, Fei
, S.
, and Zhang
, K.
, 2014
, “Stabilisation for Switched Linear Systems With Time-Varying Delay and Input Saturation
,” Int. J. Syst. Sci.
, 45
(3
), pp. 532
–546
.16.
Zhang
, J.
, Han
, Z.
, Zhu
, F.
, and Zhao
, Z.
, 2014
, “Absolute Exponential Stability and Stabilization of Switched Nonlinear Systems
,” Syst. Control Lett.
, 66
, pp. 51
–57
.17.
Shen
, J.
, and Hu
, J.
, 2012
, “Stability of Discrete-Time Switched Homogeneous Systems on Cones and Conewise Homogeneous Inclusions
,” SIAM J. Control Optim.
, 50
(4
), pp. 2216
–2253
.18.
Aleksandrov
, A. Y.
, Kosov
, A. A.
, and Platonov
, A. V.
, 2012
, “On the Asymptotic Stability of Switched Homogeneous Systems
,” Syst. Control Lett.
, 61
(1
), pp. 127
–133
.19.
Xiang
, W.
, and Xiao
, J.
, 2014
, “Stabilization of Switched Continuous-Time Systems With all Modes Unstable Via Dwell Time Switching
,” Automatica
, 50
(3
), pp. 940
–945
.20.
Li
, Z.
, Gao
, H.
, Agarwal
, R.
, and Kaynak
, O.
, 2013
, “H∞ Control of Switched Delayed Systems With Average Dwell Time
,” Int. J. Control
, 86
(12
), pp. 2146
–2158
.21.
Duan
, C.
, and Wu
, F.
, 2014
, “Analysis and Control of Switched Linear Systems Via Dwell-Time Min-Switching
,” Syst. Control Lett.
, 70
, pp. 8
–16
.22.
Yu
, X.
, Wu
, C.
, Liu
, F.
, and Wu
, L.
, 2013
, “Sliding Mode Control of Discrete-Time Switched Systems With Time-Delay
,” J. Franklin Inst.
, 350
(1
), pp. 19
–33
.23.
Sun
, Z.
, and Ge
, S. S.
, 2005
, “Analysis and Synthesis of Switched Linear Control Systems
,” Automatica
, 41
(2
), pp. 181
–195
.24.
Zhao
, X.
, Zheng
, X.
, Niu
, B.
, and Liu
, L.
, 2015
, “Adaptive Tracking Control for a Class of Uncertain Switched Nonlinear Systems
,” Automatica
, 41
, pp. 185
–191
.25.
Xiang
, W.
, and Xiao
, J.
, 2012
, “Stability Analysis and Control Synthesis of Switched Impulsive Systems
,” Int. J. Robust Nonlinear Control
, 22
(13
), pp. 1440
–1459
.26.
Davoodi
, M. R.
, Golabi
, A.
, Talebi
, H. A.
, and Momeni
, H. R.
, 2012
, “Simultaneous Fault Detection and Control Design for Switched Linear Systems: A Linear Matrix Inequality Approach
,” ASME J. Dyn. Syst. Meas. Control
, 134
(6
), p. 061010
.27.
Dong
, X.
, and Zhao
, J.
, 2013
, “Robust Output Tracking Control for a Class of Uncertain Switched Nonlinear Systems
,” ASME J. Dyn. Syst. Meas. Control
, 135
(3
), p. 031001
.28.
Alessandri
, A.
, and Coletta
, P.
, 2001
, “Switching Observers for Continuous-Time and Discrete-Time Linear Systems
,” American Control Conference
, Arlington, TX
, pp. 2516
–2521
.29.
Pettersson
, S.
, 2006
, “Designing Switched Observers for Switched Systems Using Multiple Lyapunov Functions and Dwell-Time Switching
,” 2nd IFAC Conference on Analysis and Design of Hybrid Systems
, Alghero, Italy
, pp. 18
–23
.30.
Tian
, Y.
, Floquet
, T.
, Belkoura
, L.
, and Perruquetti
, W.
, 2011
, “Algebraic Switching Time Identification for a Class of Linear Hybrid Systems
,” Nonlinear Anal. Hybrid Syst.
, 5
(2
), pp. 233
–241
.31.
Bejarano
, F. J.
, Pisano
, A.
, and Usai
, E.
, 2011
, “Finite-Time Converging Jump Observer for Switched Linear Systems With Unknown Inputs
,” Nonlinear Anal. Hybrid Syst.
, 5
(2
), pp. 174
–188
.32.
Xiang
, M.
, and Xiang
, Z.
, 2013
, “Observer Design of Switched Positive Systems With Time-Varying Delays
,” Circuits Syst. Signal Process.
, 32
(5
), pp. 2171
–2184
.33.
Zhao
, X.
, Liu
, H.
, Zhang
, J.
, and Li
, H.
, 2015
, “Multiple-Mode Observer Design for a Class of Switched Linear Systems
,” IEEE Trans. Autom. Sci. Eng.
, 12
(1
), pp. 272
–280
.34.
Tanwani
, A.
, Shim
, H.
, and Liberzon
, D.
, 2013
, “Observability for Switched Linear Systems: Characterization and Observer Design
,” IEEE Trans. Autom. Control
, 58
(4
), pp. 891
–904
.35.
Zhang
, L.
, Zhuang
, S.
, and Shi
, P.
, 2015
, “Non-Weighted Quasi-Time-Dependent H∞ Filtering for Switched Linear Systems With Persistent Dwell-Time
,” Automatica
, 54
, pp. 201
–209
.36.
Germani
, A.
, Manes
, C.
, and Palumbo
, P.
, 2009
, “State Estimation of Stochastic Systems With Switching Measurements: A Polynomial Approach
,” Int. J. Robust Nonlinear Control
, 19
(14
), pp. 1632
–1655
.37.
Yang
, J.
, Chen
, Y.
, and Wang
, X.
, 2015
, “Active Mode Identification and Continuous State Estimation for Switched Linear Systems With Unknown Inputs and Slow Switching Signal
,” Circuits Syst. Signal Process.
, 34
(7
), pp. 2193
–2211
.38.
Barbot
, J. P.
, Saadaoui
, H.
, Djemai
, M.
, and Manamanni
, N.
, 2007
, “Nonlinear Observer for Autonomous Switching Systems With Jumps
,” Nonlinear Anal. Hybrid Syst.
, 1
(4
), pp. 537
–547
.39.
Yang
, J.
, Chen
, Y.
, Zhu
, F.
, Yu
, K.
, and Bu
, X.
, 2015
, “Synchronous Switching Observer for Nonlinear Switched Systems With Minimum Dwell Time Constraint
,” J. Franklin Inst.
, 352
(11
), pp. 4665
–4681
.40.
Corless
, M.
, and Tu
, J.
, 1998
, “State and Input Estimation for a Class of Uncertain Systems
,” Automatica
, 34
(6
), pp. 757
–764
.41.
Xiang
, W.
, and Xiao
, J.
, 2013
, “Finite-Time Stability and Stabilisation for Switched Linear Systems
,” Int. J. Syst. Sci.
, 44
(2
), pp. 384
–400
.Copyright © 2016 by ASME
You do not currently have access to this content.
