© The Institution of Engineering and Technology
In this study, a stability criterion and robust ℋ∞ mode delay-dependent quantised dynamic output feedback controller design problem for discrete-time systems with random communication delays, packet dropouts and quantisation errors are investigated. Random communication delays from the sensor to controller network are modelled using a finite-state Markov chain with a special transition probability. A logarithmic quantiser is used to quantise the measured output. The Lyapunov–Krasovskii (L–K) functional approach is used to derive the stochastic stability criterion for the system with a given attenuation level. Sufficient conditions for the existence of an output feedback controller is formulated in terms of bilinear matrix inequalities (BMIs). Owing to the special transition probability matrix, a new slack matrix is added to BMIs to relax the sufficient conditions for the existence of an output feedback controller. Furthermore, an iterative algorithm is used to convert the BMIs into the quasi-convex optimisation problem which can be solved easily. An example is given to demonstrate the effectiveness of the proposed design.
References
-
-
1)
-
Xiao, L., Hassibi, A., How, J.: `Control with random communication delays via a discrete-time jump system approach', Proc. 2000 American Control Conf., 2000, 3, p. 2199–2204.
-
2)
-
E.K. Boukas ,
P. Shi ,
M. Karan ,
C.Y. Kaya
.
Linear discrete-time systems with Markovian jumps and mode dependent time-delay: stability and stabilizability.
Math. Probl. Eng.
,
2 ,
123 -
133
-
3)
-
M. Fu ,
L. Xie
.
The sector bound approach to quantized feedback control.
IEEE Trans. Autom. Control
,
1698 -
1711
-
4)
-
Z.H. Guan ,
W.H. Chen ,
J.X. Xu
.
Delay-dependent stability and stabilizability of uncertain jump bilinear stochastic systems with mode-dependent time-delays.
Int. J. Syst. Sci.
,
5 ,
275 -
285
-
5)
-
Zhang, Y., Zhong, Q.: `Stability of networked control systems with communication constraints', 2008 Chinese Control and Decision Conf., 2008, p. 335–339.
-
6)
-
I.V. Kolmanovsky ,
T.L. Maizenberg
.
Optimal control of continuous-time linear systems with a time-varying, random delay.
Syst. Control Lett.
,
2 ,
119 -
126
-
7)
-
D. Srinivasagupta ,
H. Schättler ,
B. Joseph
.
Time-stamped model predictive control: an algorithm for control of processes with random delays.
Comput. Chem. Eng.
,
8 ,
1337 -
1346
-
8)
-
S. Hu ,
W.-Y. Yan
.
Stability robustness of networked control systems with respect to packet loss.
Automatica
,
7 ,
1243 -
1248
-
9)
-
D. Huang ,
S.K. Nguang
.
State feedback control of uncertain networked control systems with random time delays.
IEEE Trans. Autom. Control
,
3 ,
829 -
834
-
10)
-
E.K. Boukas ,
Z.K. Liu
.
Robust stability and stabilizability of Markov jump linear uncertain systems with mode-dependent time delays.
J. Optim. Theory Appl.
,
3 ,
587 -
600
-
11)
-
Goncalves, A.P.C., Fioravanti, A.R., Geromel, J.C.: `Dynamic output feedback ℋ', Proc. 47th IEEE Conf. on Decision and Control, 2008, Cancun, Mexico, p. 4787–4792.
-
12)
-
D. Yue ,
C. Peng ,
G.Y. Tang
.
Guaranteed cost control of linear systems over networks with state and input quantizations.
IEE Proc. Control Theory Appl.
,
2 ,
658 -
664
-
13)
-
Z.D. Wang ,
J. Lam ,
X.H. Liu
.
Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances.
IEEE Trans. Circuits Syst.
,
262 -
268
-
14)
-
S.Y. Xu ,
J. Lam ,
X.R. Mao
.
Delay-dependent ℋ1 control and filtering for unertain Markovian jump systems with time-varying delays.
IEEE Trans. Circuits Syst.
,
561 -
566
-
15)
-
Chen, W.H., Zheng, W.X.: `Robust stabilization of delayed Markovian jump systems subject to parametric uncertainties', Proc. 46th IEEE Conf. on Decision and Control, 2007, New Orleans, LA, USA, p. 3054–3059.
-
16)
-
Z. Wang ,
F. Yang
.
Robust filtering for uncertain linear systems with delayed states and outputs.
IEEE Trans. Circuits Syst. I, Fundam. Theory Appl.
,
1 ,
125 -
130
-
17)
-
E. Tian ,
D. Yue ,
C. Peng
.
Quantized output feedback control for networked control systems.
Inf. Sci.
,
2734 -
2749
-
18)
-
Yufeng, W., Changhong, W., Xu, H.: `Guaranteed cost control with random communication delays via jump linear system approach', Eighth Control, Automation, Robotics and Vision Conf., 2004, 1, p. 298–303.
-
19)
-
C. Peng ,
Y.-C. Tian
.
Networked ℋ∞ control of linear systems with state quantization.
Inf. Sci.
,
5763 -
5774
-
20)
-
W. Zhang ,
M.S. Branicky ,
S.M. Philips
.
Stability of networked control systems.
IEEE Control Syst. Mag.
,
1 ,
84 -
99
-
21)
-
E.G. Laurent ,
O. Francois ,
A. Mustapha
.
A cone complementarity linearization algorithm for static output-feedback and related problems.
IEEE Trans. Autom. Control
,
8 ,
1171 -
1176
-
22)
-
F. Yang ,
Z. Wang ,
Y. Hung ,
M. Gani
.
ℋ∞ control for networked systems with random communication delays.
IEEE Trans. Autom. Control
,
3 ,
511 -
518
-
23)
-
Y.Y. Cao ,
J. Lam
.
Delay-dependent stochastic stability and ℋ∞ analysis for time-delay systems with Markovian jumping parameters.
J. Franklin Inst.
,
423 -
434
-
24)
-
J.F. Hayes
.
(1984)
Modeling and analysis of computer communications networks.
-
25)
-
E. Tian ,
D. Yue ,
X. Zhao
.
Quantised control design for networked control systems.
IET Control Theory Appl.
,
1693 -
1699
-
26)
-
Gao, H., Chen, T., Lam, J.: `A new model for time-delay systems with application to network based control', 2006 Chinese Control Conf., 2006, p. 56–61.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2009.0222
Related content
content/journals/10.1049/iet-cta.2009.0222
pub_keyword,iet_inspecKeyword,pub_concept
6
6