© The Institution of Engineering and Technology
The problem of robust state feedback control using delta operator approach for a class of linear fractional uncertain systems with timevarying delays is investigated. Based on Lyapunov–Krasovskii functional in delta domain, a new delaydependent state feedback controller is presented in terms of linear matrix inequalities. The samplingperiod T is an explicit parameter, and thus it is easy to observe and analyse the effect of the state feedback controller with different sampling periods. The proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are given to illustrate the effectiveness of the developed techniques.
References


1)

G.C. Goodwin ,
R.H. Middleton
.
Rapprochement between continuous and discrete model reference adaptive control.
Automatica
,
6 ,
199 
207

2)

Z. Xiang ,
Q. Chen ,
R. Zhang
.
Robust stability analysis and control for fuzzy systems with uncertainties using the delta operator.
Control Decis.
,
6 ,
720 
723

3)

D. Li ,
S. Fei
.
Robust stabilization for delta operator based systems.
Fuzzy Syst. Math.
,
2 ,
140 
145

4)

S. Chen ,
R.H. Istepanian ,
J. Wu ,
J. Chu
.
Comparative study on optimizing closedloop stability bounds of finiteprecision controller structures with shift and delta operators.
Syst. Control Lett.
,
3 ,
153 
163

5)

W. Ebert
.
Optimal filtered predictive control a delta operator approach.
Syst. Control Lett.
,
1 ,
69 
80

6)

P. Suchomski
.
Numerically robust deltadomain solutions to discretetime Lyapunov equations.
Syst. Control Lett.
,
4 ,
319 
326

7)

H. Fan
.
Singular root distribution problem for deltaoperator based real polynomials.
Automatica
,
5 ,
791 
807

8)

C.B. Soh
.
Robust discrete time systems using delta operator.
Int. J. Control
,
2 ,
453 
464

9)

C.B. Soh
.
Robust stability of discretetime systems using delta operator.
IEEE Trans. Autom. Control
,
3 ,
377 
380

10)

G. Emmanuel ,
J. Collins ,
T. Song
.
A delta operator approach to discretetime H∞ control.
Int. J. Control
,
4 ,
315 
320

11)

Y. Xia ,
P. Shi ,
G.P. Liu ,
D. Rees ,
J. Han
.
Active disturbance rejection control for uncertain multivariable systems with timedelay.
IET Proc. Control Theory Appl.
,
1 ,
75 
81

12)

Y.Q. Xia ,
Y.M. Jia
.
Robust slidingmode control for uncertain timedelay systems: an LMI approach.
IEEE Trans. Autom. Control
,
6 ,
1086 
1092

13)

Y. Xia ,
Y. Jia
.
Robust control of state delayed systems with polytopic type uncertainties via parameterdependent Lyapunov functionals.
Syst. Control Lett.
,
3 ,
183 
193

14)

Y. Xia ,
Y. Jia
.
Robust stability analysis for timedelay systems with polytopic uncertainties via parameterdependent Lyapunov functionals.
Int. J. Control
,
1427 
1434

15)

E.K. Boukas ,
N.F. AlMuthairi
.
Delaydependent stabilization of singular linear systems with delays.
Int. J. Innovative Comput. Inf. Control
,
2 ,
283 
291

16)

E.K. Boukas
.
State feedback stabilization of nonlinear discretetime systems with timevarying time delay.
Nonlinear Anal.
,
6 ,
1341 
1350

17)

Y. Sun ,
L. Wang ,
G. Xie
.
Delaydependent robust stability and stabilization for discretetime switched systems with modedependent timvarying delays.
Appl. Math. Comput.
,
2 ,
428 
435

18)

S. Xu ,
T. Chen
.
Robust H∞ control for uncertain discretetime systems with timevarying delays via exponential output feedback controllers.
Syst. Control Lett.
,
171 
183

19)

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

20)

H. Gao ,
C. Wang
.
A delaydependent approach to robust ℋ∞ filtering for uncertain discretetime statedelayed systems.
IEEE Trans. Signal Process.
,
1631 
1640

21)

Jiang, X., Han, Q., Yu, X.: `Stability criteria for linear discretetime systems with intervallike timevarying delay', American Control Conf., June 2005, Portland, OR, USA, p. 2817–2822.

22)

L. Xie
.
Output feedback H∞ control of systems with parameter uncertainty.
Int. J. Control
,
4 ,
741 
750

23)

H. Gao ,
J. Lam ,
C. Wang ,
Y. Wang
.
Delaydependent outputfeedback stabilization of discretetime systems with timevarying state delay.
IEE Proc. Control Theory Appl.
,
6 ,
691 
698

24)

K. Tanaka ,
M. Sano
.
A robust stabilization problem of fuzzy control systems and its application to backing up control of a trucktrailer.
IEEE Trans. Fuzzy Syst.
,
2 ,
119 
133

25)

Y.Y. Cao ,
P.M. Frank
.
Stability analysis and synthesis of nonlinear timedelay systems via linear Takagi–Sugeno fuzzy models.
Fuzzy Sets Syst.
,
213 
229
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta_20070070
Related content
content/journals/10.1049/ietcta_20070070
pub_keyword,iet_inspecKeyword,pub_concept
6
6