© The Institution of Engineering and Technology
The problem of delaydependent robust energytopeak filtering design for a class of discretetime switched linear systems with a timevarying state delay and polytopic uncertainties is revisited. The objective is to design a homogeneous switched linear filter guaranteeing the exponential stability of the resulting filtering error system with a minimised robust energytopeak disturbance attenuation level under average dwelltime switching scheme. Based on a novel delay and parameterdependent discontinuous switched Lyapunov–Krasovskii functional combined with Finsler's lemma, a new sufficient condition for robust exponential stability and energytopeak performance analysis is first derived and then the corresponding filter synthesis is developed. It is shown that the filter parameters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach in comparison with the existing approaches.
References


1)

Hespanha, J.P., Morse, A.S.: `Stability of switched systems with average dwelltime', In Proceedings of the 38th IEEE Conf. Decision and Control, 1999, Phoenix, Arizona, USA, p. 2655–2660.

2)

D. Liberzon ,
A.S. Morse
.
Basic problems in stability and design of switched systems.
IEEE Control Syst. Mag.
,
5 ,
59 
70

3)

Decarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B.: `Perspectives and results on the stability and stabilizability of hybrid systems', Proc. IEEE, Special Issue on Hybrid Systems, 2000, 88, p. 1069–1082.

4)

Z. Sun ,
S.S. Ge
.
Analysis and synthesis of switched linear control systems.
Automatica
,
2 ,
181 
195

5)

G. Xie ,
L. Wang
.
Controllability and stabilizability of switched linear systems.
Syst. Control Lett.
,
2 ,
135 
155

6)

M.S. Branicky
.
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems.
IEEE Trans. Autom. Control
,
4 ,
475 
482

7)

H. Ye ,
A.N. Michel ,
L. Hou
.
Stability theory for hybrid dynamical systems.
IEEE Trans. Autom. Control
,
4 ,
461 
474

8)

J. Daafouz ,
P. Riedinger ,
C. Iun
.
Stability analysis and control synthesis for switched systems: a switched lyapunov function approach.
IEEE Trans. Autom. Control
,
11 ,
1883 
1887

9)

Fang, L., Lin, H., Antsaklis, P.J.: `Stabilization and performance analysis for a class of switched systems', Proc. 43rd IEEE Conf. Decision and Control, 2004, Atlantis, Paradise Island, Bahamas, p. 3265–3270.

10)

D. Xie ,
L. Wang ,
F. Hao ,
G. Xie
.
LMI approach to L2gain analysis and control synthesis of uncertain switched systems.
IEE Proc. Control Theory and Appl.
,
1 ,
21 
28

11)

N.H. ElFarra ,
P. Mhaskar ,
P.D. Christofides
.
Output feedback control of switched nonlinear systems using multiple Lyapunov functions.
Syst. Control Lett.
,
12 ,
1163 
1182

12)

H. Lin ,
P.J. Antsaklis
.
Switching stabilizability for continuoustime uncertain switched linear systems.
IEEE Trans. Autom. Control
,
4 ,
633 
646

13)

L. Zhang ,
P. Shi ,
C. Wang ,
H. Gao
.
Robust ℋ∞ filtering for switched linear discretetime systems with polytopic uncertainties.
Int. J. Adaptive Control Signal Process.
,
6 ,
291 
304

14)

L. Zhang ,
E.K. Boukas ,
P. Shi
.
Exponential ℋ∞ filtering for uncertain discretetime switched linear systems with average dwell time: a μdependent approach.
Int. J. Robust Nonlinear Control
,
11 ,
1188 
1207

15)

Y.S. Moon ,
P. Park ,
W.H. Kwon ,
Y.S. Lee
.
Delaydependent robust stabilization of uncertain statedelayed systems.
Int. J. Control
,
14 ,
1447 
1455

16)

E. Fridman ,
U. Shaked
.
A descriptor system approach to ℋ∞ control of linear timedelay systems.
IEEE Trans. Autom. Control
,
253 
270

17)

H. Gao ,
T. Chen
.
New results on stability of discretetime systems with timevarying state delay.
IEEE Trans. Autom. Control
,
2 ,
328 
334

18)

Y. He ,
Q. Wang ,
C. Lin ,
M. Wu
.
Delayrangedependent stability for systems with timevarying delay.
Automatica
,
2 ,
371 
376

19)

J. Qiu ,
G. Feng ,
J. Yang
.
Improved delaydependent ℋ∞ filtering for discretetime polytopic linear delay systems.
IEEE Trans. Circuits Syst., Part II: Express Briefs
,
2 ,
178 
182

20)

He, Y., Wu, M., Liu, G.P., She, J.H.: `Output feedback stabilization for discretetime systems with a timevarying delay', Proc. 26th Chinese Control Conf., 2007, Hunan, China, p. 64–70.

21)

C. Meyer ,
S. Schroder ,
R.W. De Doncker
.
Solidstate circuit breakers and current limiters for mediumvoltage systems having distributed power systems.
IEEE Trans. Power Electron.
,
1333 
1340

22)

D.K. Kim ,
P. Park ,
J.W. Ko
.
Output feedback ℋ∞ control of systems over communication networks using a deterministic switching system approach.
Automatica
,
7 ,
1205 
1212

23)

Z.H. Guan ,
H. Zhang ,
S.H. Yang
.
Robust passive control for Internetbased switching systems with timedelay.
Chaos Solitons Fractals
,
2 ,
479 
486

24)

Zhai, G., Sun, Y., Chen, X., Michel, A.N.: `Stability and ', Proc. 2003 American Control Conf., 2003, Denver, Colorado, USA, p. 2682–2687.

25)

Y. Sun ,
L. Wang ,
G. Xie
.
Delaydependent robust stability and H∞ control for uncertain discretetime switched systems with modedependent time delays.
Appl. Math. Comput.
,
2 ,
1228 
1237

26)

X. Liu ,
J. Shen
.
Stability theory of hybrid dynamical systems with time delay.
IEEE Trans. Autom. Control
,
4 ,
620 
625

27)

M. Sun ,
J. Zhao ,
D.J. Hill
.
Stability and ℒ2 gain for switched delay systems: a delaydependent method.
Automatica
,
10 ,
1769 
1774

28)

L. Zhang ,
P. Shi ,
E.K. Boukas ,
C. Wang
.
Robust l2l∞ filtering for switched linear discrete timedelay systems with polytopic uncertainties.
IET Control Theory Appl.
,
3 ,
722 
730

29)

X. He ,
Z. Wang ,
D. Zhou
.
Robust ℋ∞ filtering for networked systems with multiple state delays.
Int. J. Control
,
8 ,
1217 
1232

30)

H. Gao ,
T. Chen ,
J. Lam
.
A new delay system approach to networkbased control.
Automatica
,
1 ,
39 
52

31)

S. Boyd ,
L. Ghaoui ,
E.L. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequality in systems and control theory.

32)

M.C. de Oliveira ,
R.E. Skelton ,
S.O.R. Moheimani
.
(2001)
Stability tests for constrained linear systems, Perspectives in robust control.

33)

W.A. Zhang ,
L. Yu ,
X. Jiang
.
Delaydependent generalized H2 filtering for uncertain systems with multiple timevarying state delays.
Signal Process.
,
4 ,
709 
724

34)

H. Gao ,
J. Lam ,
C. Wang
.
Induced l2 and generalized ℋ2 filtering for systems with repeated scalar nonlinearities.
IEEE Trans. Signal Process.
,
11 ,
4215 
4226

35)

H.J. Gao ,
J. Lam ,
L.H. Xie ,
C.H. Wang
.
New approach to mixed H2/H∞ filtering for polytopic discretetime systems.
IEEE Trans. Signal Process.
,
3183 
3192

36)

H. Gao ,
J. Lam ,
C. Wang
.
Robust energytopeak filter design for stochastic timedelay systems.
Syst. Control Lett.
,
101 
111

37)

J. Xia ,
S. Xu ,
B. Song
.
Delaydependent L2−L∞ filter design for stochastic timedelay systems.
Syst. Control Lett.
,
579 
587

38)

R.C.L.F. Oliveira ,
P.L.D. Peres
.
LMI conditions for robust stability analysis based on polynomially parameterdependent Lyapunov functions.
Syst. Control Lett.
,
52 
61

39)

G. Chesi ,
A. Garulli ,
A. Tesi ,
A. Vicino
.
Robust stability of timevarying polytopic systems via parameterdependent homogeneous Lyapunov functions.
Automatica
,
2 ,
309 
316
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta_20070361
Related content
content/journals/10.1049/ietcta_20070361
pub_keyword,iet_inspecKeyword,pub_concept
6
6