© The Institution of Engineering and Technology
The problem of robust decentralised state-feedback stabilisation for discrete-time singular large-scale systems with interval uncertainties is addressed in this study. By using the matrix norm operation and the rank-1 matrix technique for interval matrices, two sufficient conditions to check the robust decentralised stabilisability of uncertain discrete-time singular large-scale systems are, respectively, obtained. At the expense of problem size (numerical complexity), the second condition gives a less conservative result than the first one. It is therefore reasonable to check the robust stabilisability by the first condition, and then if it fails, resort to the second one. Finally, illustrative examples show that the proposed conditions are effective for the design of robust decentralised stabilising state-feedback controller for not only the uncertain discrete-time singular large-scale systems but also the uncertain discrete-time regular large-scale systems.
References
-
-
1)
-
W.-J. Mao ,
J. Chu
.
Robust D-stability and D-stabilization of dynamic interval systems.
Int. J. Control Autom. Syst.
,
594 -
600
-
2)
-
C.-H. Fang ,
L. Lee ,
F.-R. Chang
.
Robust control analysis and design for discrete-time singular systems.
Automatica
,
1741 -
1750
-
3)
-
W.J. Wang ,
C.F. Cheng
.
Stabilising controller and observer synthesis for uncertain large-scale systems by the Riccati equation approach.
IEE Proc. Control Theory Appl.
,
72 -
78
-
4)
-
J.H. Park ,
S.G. Lee
.
Robust decentralized stabilization of uncertain large-scale discrete-time systems.
Int. J. Syst. Sci.
,
649 -
654
-
5)
-
H. Trinh ,
M. Aldeen
.
Decentralised feedback controllers for uncertain interconnected dynamic systems.
IEE Proc. Control Theory Appl.
,
429 -
434
-
6)
-
Chen, C.-T., Zhao, J.-C.: `Stability of a kind of continuous singular large-scale dynamical systems', Proc. Sixth Int. Conf. on Machine Learning and Cybernetics, 2007, Hong Kong, China, p. 2317–2321.
-
7)
-
D.D. Siljak
.
(1978)
Large-scale dynamic systems: stability and structure.
-
8)
-
I.R. Petersen
.
A stabilization algorithm for a class of uncertain linear systems.
Syst. Control Lett.
,
351 -
357
-
9)
-
P. Gahinet ,
P. Apkarian ,
M. Chilali
.
Affine parameter-dependent Lyapunov functions and real parametric uncertainty.
IEEE Trans. Autom. Control
,
436 -
442
-
10)
-
S. Wo ,
Y. Zou ,
M. Sheng ,
S. Xu
.
Robust control for discrete-time singular large-scale systems with parameter uncertainty.
J. Franklin Inst.
,
97 -
106
-
11)
-
S. Xu ,
J. Lam
.
Robust stability and stabilization of discrete singular systems: an equivalent characterization.
IEEE Trans. Autom. Control
,
568 -
574
-
12)
-
X. Ji ,
H. Su ,
J. Chu
.
Robust state feedback H∞ control for uncertain linear discrete singular systems.
IET Control Theory Appl.
,
195 -
200
-
13)
-
D.D. Siljak ,
A.I. Zecevic
.
Control of large-scale systems: beyond decentralized feedback.
Ann. Rev. Control
,
169 -
179
-
14)
-
L. Dai
.
(1989)
Singular control systems.
-
15)
-
S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.
-
16)
-
G. Zhang ,
Y. Xia ,
P. Shi
.
New bounded real lemma for discrete-time singular systems.
Automatica
,
886 -
890
-
17)
-
W.-J. Mao ,
J. Chu
.
Quadratic stability and stabilization of dynamic interval systems.
IEEE Trans. Autom. Control
,
1007 -
1012
-
18)
-
J. Daafouz ,
J. Bernussou
.
Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties.
Syst. Control Lett.
,
355 -
359
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2008.0600
Related content
content/journals/10.1049/iet-cta.2008.0600
pub_keyword,iet_inspecKeyword,pub_concept
6
6