This paper is concerned with the problem of delay-dependent robust stability for uncertain discrete singular systems with time-varying delays. Without introducing the free-weighting matrices to deal with the cross terms, a new and improved delay-dependent condition is established for the nominal systems to be regular, causal, and stable via a new Lyapunov function employing the integrated lower and upper time-delay bounds. The condition is also extended to the uncertain case. A numerical example is given to illustrate that the proposed methods are effective and lead to less conservatism than the existing ones.
DaiL.Singular control systems, (Springer-Verlag, Berlin1989)
2.
XuS.LamJ.Robust control and filtering of singular systems (Springer-Verlag, Berlin2006)
3.
FridmanE.ShakedU. ‘H∞ control of linear state-delay descriptor systems: an LMI approach.’ Linear Algebr. Appli. 351-352 (2002): 271–302
4.
BoukasE. K.LiuZ. K.‘Delay-dependent stabilization of singularly perturbed jump linear systems.’Int. J. Control77 (2004): 310–319
5.
BoukasE. K.Al-MuthairiN. F.‘Delay-dependent stabilization of singular linear systems with delays.’Int. J. Innov. Comput., Infor. Control53 (2006): 283–291
6.
YueD.HanQ.‘Delay-dependent robust H∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays.’IEE Proc. D, Control Theory Appli.152 (2005): 628–638
7.
YueD.LamJ.HoD. W. C.‘Delay-dependent robust exponential stability of uncertain descriptor systems with time-varying delays.’Dyn. Continuous, Discrete Impulsive Syst. B: Appli. Algorithms12 (2005): 129–150
8.
YangF.ZhangQ.‘Delay-dependent H∞ control for linear descriptor systems with delay in state.’J. Control Theory Appli.3 (2005): 76–84
9.
ZhuS.ZhangC.ChengZ.FengJ.‘Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems.’IEEE Trans. Autom. Control52 (2007): 880–885
10.
XuS.LamJ.ZouY.‘An improved characterization of bounded realness for singular delay systems and its applications.’Int. J. Robust Nonlinear Control18 (2008): 263–277
11.
WuZ.ZhouW.‘Delay-dependent robust H∞ control for uncertain singular time-delay systems.’IET Control Theory Appli.1 (2007): 1234–1241
12.
WuM.HeY.SheJ. H.LiuG. P.‘Delay-dependent criteria for robust stability of time-varying delay systems.’Automatica40 (2004): 1435–1439
13.
HeY.WuM.SheJ. H.LiuG. P.‘Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays.’Syst. Control Lett.51 (2004): 57–65
14.
HeY.WangQ. G.XieL. H.LinC.‘Further improvement of free-weighting matrices technique for systems with time-varying delay.’IEEE Trans. Autom. Control52 (2007): 293–299
15.
HeY.WangQ. G.LinC.‘An improved H∞ filter design for systems with time-varying interval delay.’IEEE Trans. Circuits and Systems II: Express Briefs53 (2006): 1235–1239
16.
HeY.WuM.LiuG. P.SheJ. H.‘Output feedback stabilization for a discrete-time system with a time-varying delay.’IEEE Trans. Autom. Control35 (2008): 2327–2377
17.
JiX.SuH.ChuJ.‘An LMI approach to robust stability of uncertain discrete singular time-delay systems.’Asian J. Control8 (2006): 56–62
18.
WuZ.SuH.ChuJ.‘Robust stabilization for uncertain discrete singular systems with state delay.’Int. J. Robust Nonlinear Control18 (2008): 1532–1550
19.
MaS.ZhengC.ChengZ.‘Delay-dependent robust H∞ control for uncertain discrete-time singular systems with time-delays.’J. Comput. Appl. Math.217 (2008): 194–211
20.
MaS.ChengZ.ZhengC.‘Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays.’IET Control Theory Appl.1 (2007): 1086–1095
21.
XuS.LamJ.‘On equivalence and efficiency of certain stability criteria for time-delay systems.’IEEE Trans. Autom. Control52 (2007): 95–101
22.
PengC.TianY.‘Delay-dependent robust stability criteria for uncertain systems with interval time varying delay.’J. Comput. Appl. Math.214 (2008): 480–494
23.
PetersenI. R.‘A stabilization algorithm for a class of uncertain linear systems.’Syst. Control Lett.8 (1987): 351–357
24.
ZhangX.HanQ.‘A new finite sum inequality approach to delay-dependent H∞ control of discrete-time systems with time-varying delay.’Int. J. Robust Nonlinear Control18 (2008): 630–647
25.
GaoH.LamJ.ChenT.WangC.‘Stability analysis of uncertain discrete-time systems with time-varying state delay: A parameter-dependent Lyapunov function approach.’Asian J. Control8 (2006): 433–440
26.
GaoH.ChenT.‘New results on stability of discrete-time systems with time-varying state delays.’IEEE Trans. Autom. Control52 (2007): 328–334
27.
ZhangB.XuS.ZouY.‘Improved stability criterion and its applications in delayed controller design for discrete-time systems.’Automatica44 (2008): 2963–2967
