© The Institution of Engineering and Technology
This study is concerned with the problem of observer-based output feedback control for discrete-time systems with quantised inputs. Firstly, a new necessary and sufficient condition is established to guarantee the asymptotic stability of the closed-loop system. However, the condition is presented in terms of a matrix inequality that depends on quantisation parameters varying over certain intervals. To solve this problem, a new quantisation-density-dependent necessary and sufficient condition is derived. Based on such a condition, both full- and reduced-order observer-based quantised feedback controllers are designed via a single-step approach. Finally, numerical examples are given to show the effectiveness of the author's method.
References
-
-
1)
-
F. Hao ,
X. Zhao
.
Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems.
IET Control Theory Appl.
,
7 ,
1211 -
1221
-
2)
-
Z. Mao ,
B. Jiang ,
P. Shi
.
H∞ fault detection filter design for networked control systems modelled by discrete Markovian jump systems.
IET Control Theory Appl.
,
8 ,
675 -
681
-
3)
-
D. Liberzon
.
Hybrid feedback stabilization of systems with quantized signals.
Automatica
,
9 ,
1543 -
1554
-
4)
-
D.R. Quevedo ,
E.I. Silva ,
G.C. Goodwin
.
Subband coding for networked control systems.
Int. J. Robust Nonlinear Control
,
1817 -
1836
-
5)
-
D. Yue ,
Q.L. Han ,
C. Peng
.
State feedback controller design of networked control systems.
IEEE Trans. Circuits Syst. II, Exp. Briefs
,
11 ,
640 -
644
-
6)
-
Z. Wang ,
F. Yang ,
D.W.C. Ho ,
X. Liu
.
Robust H∞ control for networked systems with random packet losses.
IEEE Trans. Syst. Man Cybern. B, Cybern.
,
4 ,
916 -
924
-
7)
-
C. Peng ,
Y. Tian
.
Networked H∞ control of linear systems with state quantization.
Inf. Sci.
,
24 ,
5763 -
5774
-
8)
-
Y. Niu ,
T.G. Jia ,
X.Y. Wang ,
F. Yang
.
Output-feedback control design for ncss subject to quantization and dropout.
Inf. Sci.
,
21 ,
3804 -
3813
-
9)
-
X. Liu ,
Q. Zhang
.
New approaches to controller designs based on fuzzy observers for T-S fuzzy systems via LMI.
Automatica
,
9 ,
1571 -
1582
-
10)
-
H. Gao ,
T. Chen
.
A new approach to quantized feedback control systems.
Automatica
,
2 ,
534 -
542
-
11)
-
B. Picasso ,
A. Bicchi
.
On the stabilization of linear systems under assigned I/O quantization.
IEEE Trans. Autom. Control
,
10 ,
1994 -
2000
-
12)
-
C. Lin ,
Q.G. Wang ,
T.H. Lee ,
Y. He ,
B. Chen
.
Observer-based H∞ fuzzy control design for T-S fuzzy systems with state delays.
Automatica
,
868 -
874
-
13)
-
F. Fagnani ,
S. Zampieri
.
Stability analysis and synthesis for scalar linear systems with a quantized feedback.
IEEE Trans. Autom. Control
,
9 ,
1569 -
1584
-
14)
-
D. Liberzon ,
J. Hespanha
.
Stabilization of nonlinear systems with limited information feedback.
IEEE Trans. Autom. Control
,
6 ,
910 -
915
-
15)
-
H.J. Gao ,
T.W. Chen ,
J. Lam
.
A new delay system approach to network-based control.
Automatica
,
39 -
52
-
16)
-
B. Picasso ,
A. Bicchi ,
A. Pnueli ,
O. Maler
.
(2003)
Stabilization of LTI systems with quantized state-quantized input static feedback’, Hybrid systems: computation and control.
-
17)
-
H. Gao ,
T. Chen ,
T. Chai
.
Passivity and passification for networked control systems.
SIAM J. Control Optim.
,
4 ,
1299 -
1322
-
18)
-
Kalman, R.E.: `Nonlinear aspects of sampled-data control systems', Proc. Symp. Nonlinear Circuit Theory, 1956, Brooklyn, NY, p. 273–313.
-
19)
-
E. Tian ,
D. Yue ,
X. Zhao
.
Quantised control design for networked control systems.
IET Control Theory Appl.
,
6 ,
1693 -
1699
-
20)
-
T. Hayakawa ,
H. Ishii ,
K. Tsumura
.
Adaptive quantized control for nonlinear uncertain discrete-time systems.
Syst. Control Lett.
,
9 ,
625 -
632
-
21)
-
Y.B. Zhao ,
G.P. Liu ,
D. Rees
.
Integrated predictive control and scheduling co-design for networked control systems.
IET Control Theory Appl.
,
1 ,
7 -
15
-
22)
-
Y. Xia ,
G.P. Liu ,
M. Fu ,
D. Rees
.
Predictive control of networked systems with random delay and data dropout.
IET Control Theory Appl.
,
11 ,
1476 -
1486
-
23)
-
Minami, Y., Azuma, S., Sugie, T.: `An optimal dynamic quantizer for feedback control with discrete-valued signal constraints', Proc. 46th IEEE Conf. on Decision and Control, 2007, New Orleans, p. 2259–2264.
-
24)
-
Y. Zou ,
T. Chen ,
S. Li
.
Network-based predictive control of multirate systems.
IET Control Theory Appl.
,
7 ,
1145 -
1156
-
25)
-
D.F. Delchamps
.
Stabilizing a linear system with quantized state feedback.
IEEE Trans. Autom. Control
,
8 ,
916 -
924
-
26)
-
M. Fu ,
L. Xie
.
The sector bound approach to quantized feedback control.
IEEE Trans. Autom. Control
,
11 ,
1698 -
1711
-
27)
-
T. Hayakawa ,
H. Ishii ,
K. Tsumura
.
Adaptive quantized control for linear uncertain discrete-time systems.
Automatica
,
3 ,
692 -
700
-
28)
-
T.C. Yang ,
C. Peng ,
D. Yue ,
M.R. Fei
.
New study of controller design for networked control systems.
IET Control Theory Appl.
,
7 ,
403 -
412
-
29)
-
S. Chae ,
F. Rasool ,
S.K. Nguang ,
A. Swain
.
Robust mode delay-dependent H∞ control of discrete-time systems with random communication delays.
IET Control Theory Appl.
,
6 ,
936 -
944
-
30)
-
R.W. Brockett ,
D. Liberzon
.
Quantized feedback stabilization of linear systems.
IEEE Trans. Autom. Control.
,
7 ,
1279 -
1289
-
31)
-
Yue, D., Peng, C., Yang, G.: `Guaranteed cost control of linear systems over networks with state and input quantisations', IEE Proc. Control Theory and Applications, 2006, 153, p. 658–664.
-
32)
-
X.M. Sun ,
G.P. Liu ,
W. Wang ,
D. Rees
.
Stability analysis for networked control systems based on event-time-driven mode.
Int. J. Control
,
12 ,
2260 -
2266
-
33)
-
Liu, M., Ho, D.W.C., Lu, J.Q.: `On quantized control for Markovian jump linear system over networks with limited information', Proc. Seventh Asian Control Conf., 2009, Hong Kong, p. 226–231.
-
34)
-
N. Elia ,
S.K. Mitter
.
Stabilization of linear systems with limited information.
IEEE Trans. Autom. Control.
,
9 ,
1384 -
1400
-
35)
-
W.W. Che ,
G.H. Yang
.
Quantised H∞ filter design for discrete-time systems.
Int. J. Control
,
2 ,
195 -
206
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2010.0148
Related content
content/journals/10.1049/iet-cta.2010.0148
pub_keyword,iet_inspecKeyword,pub_concept
6
6