This paper proposes new stability conditions for linear systems with a time-varying state delay. The time-varying delay is treated as a polytopic uncertainty parameter, and a Lyapunov functional that is dependent on the delay parameter is constructed. Linear matrix inequality conditions of system stability and robust stability are derived. Numerical and practical examples are given to show the effectiveness and non-conservativeness of the proposed conditions.
FridmanE.ShakedU.Delay-dependent stability and H∞ control: constant and time-varying delays.’Int. J. Control2003, 76(1), 48–60.
6.
XuS.LamJ.ZouY.New results on delay-dependent robust H∞ control for systems with time-varying delays.’Automatica2006, 42(2), 343–348.
7.
WuM.HeY.SheJ.-H.Liu, Delay-dependent criteria for robust stability of time-varying delays systems. Automatica2004, 40(8), 1435–1439.
8.
JiangX.HanQ.-L.On H∞ control for linear systems with interval time-varying delay. Automatica2005, 41(12), 2099–2106.
9.
JiangX.HanQ.-L.Delay-dependent robust stability for uncertain linear systems with interval time-varying delay. Automatica, 2006, 42(6), 1059–1065.
10.
LinC.WangQ.-G.LeeT.-H.A less conservative robust stability test for linear uncertain time-delay systems. IEEE Trans. Autom. Control2006, 51(1), 87–91.
11.
HeY.WangQ.-G.LinC.WuM.‘Delay-range-dependent stability for systems with time-varying delay. Automatica2007, 43(2), 371–376.
12.
HeY.WangQ.-G.XieL.LinC.Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control2007, 52(2), 293–299.
13.
ParkP.KoJ. W.Stability and robust stability for systems with a time-varying delay. Automatica2007, 43(10), 1855–1858.
14.
FridmanE.SeuretA.RichardJ. P.Robust sampled-data stabilization of linear systems: An input delay approach. Automatica2004, 40(8), 1441–1446.
15.
ShaoH.New delay-dependent stability criteria for systems with interval delay. Automatica2009, 45(3), 744–749.
16.
PengC.TianY.-C.Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. IET Control Theory Appl.2008, 2(9), 752–761.
17.
BarmishB. R.New tools for robustness of linear systems1994,(Macmillan, New York, New York).
18.
XieL.Output feedback Hinfin; control of systems with parameter uncertainty. Int. J. Control1996, 63(4), 741–750.
19.
BoydS.El GhaouiL.FeronE.BalakrishnanV.Linear matrix inequalities in system and control theory1994 (SIAM, Philadelphia, Pennsylvania).
