This paper deals with delay-dependent H∞ control for discrete-time systems with time-varying state delays and input delays. A new finite-sum inequality is first established to derive a delay-dependent condition, under which the resulting closed-loop system via a state feedback is asymptotically stable with a prescribed H∞ noise attenuation level. Moreover, a modified iterative algorithm according to the previously published algorithm of Ghaoui and Oustry (IEEE Trans. Autom. Control, 1997, 42(8), 1171–1176) involving convex optimization is proposed to obtain a suboptimal H∞ controller. Two numerical examples are presented which show the effectiveness of the proposed method.
QiuJ.ZhangJ.ShiP.Robust stability of uncertain linear systems with time-varying delay and non-linear perturbations. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 2006, 220(5), 411–416.
2.
SunY.WangL.XieG.Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. Appl. Math. Comput., 2006, 180(2), 428–435.
3.
XuS.ChenT.Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers. Syst. Control Lett., 2004, 51(3), 171–183.
4.
MoheimaniS.SavkinV.PetersenI.Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty. Int. J. Robust Nonlinear Control, 2000, 31(1), 137–147.
5.
GermaniA.PepeP.OlivierS.A state observer for a class of nonlinear systems with multiple discrete and distributed time delays. Eur. J. Control, 2005, 11(3), 196–208.
6.
ChenJ.Robust output observer-based control of neutral uncertain systems with discrete and distributed time delays: LMI optimization approach. Chaos, Solitons Fractals, 2007, 34(4), 1254–1264.
7.
MahmoudM.MuthairiN.Quadratic stabilization of continuous time systems with state delay and norm-bounded time-varying uncertainties. IEEE Trans. Autom. Control, 1994, 39(1), 2135–2139.
8.
PhoojaruenchanachaiS.FurutaK.Memory-less stabilization of uncertain linear systems including time-varying state delays. IEEE Trans. Autom. Control, 1992, 37(2), 1022–1026.
9.
FridmanE.ShakedU.A descriptor system approach to HN control of linear time-delay systems. IEEE Trans. Autom. Control, 2002, 47(3), 253–270.
10.
FridmanE.ShakedU.An improved stabilization method for linear time-delay systems. IEEE Trans. Autom. Control, 2002, 47(3), 1931–1937.
11.
MoonY.ParkP.KwonW.LeeY.Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control, 2001, 74(4), 1447–1455.
12.
ChenW.XuJ.GuanZ.Guaranteed cost control for uncertain Markovian jump systems with mode-dependent delays. IEEE Trans. Autom. Control, 2003, 48(2), 2270–2277.
13.
ChenW.GuanZ.LuX.Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems. Automatica, 2004, 40(2), 1263–1268.
14.
ChenW.GuanZ.LuX.Delay-dependent guaranteed cost control for discrete-time uncertain system with delay. IEE Proc. Control Theory Applic., 2003, 150(2), 412–416.
15.
XuS.LambJ.ZouaY.New results on delay-dependent robust H∞ control for systems with time-varying delays. Automatica, 2006, 42(2), 343–348.
16.
YueD.HanQ.Delay-dependent robust H∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays. IEE Proc. Control Theory Applic., 2005, 152(6), 628–638.
17.
PalharesR.CamposC.EkelP.LelesM.AngeloM.Delay-dependent robust H∞ control of uncertain linear systems with time-varying delays. Comput. Math. Applic., 2005, 50(2), 13–32.
18.
HsiaoF.Robust H∞ fuzzy control of nonlinear systems with multiple time delays. Int. J. Syst. Sci., 2007, 38(4), 351–360.
19.
XuS.LamJ.GaoH.ZouY.Robust H∞ filtering for uncertain discrete stochastic systems with time delays. Circuits, Syst. Signal Processing, 2005, 24(6), 753–770.
20.
CaoY.FrankP.Robust control for uncertain discrete-time jump linear systems with time delay. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 1999, 213(6), 477–488.
21.
PlummerA.LingC.Stability and robustness for discrete-time systems with control signal saturation. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 2000, 214(1), 65–76.
22.
ChenS.Robust D-stability analysis for linear discrete-time singular systems with structured parameter uncertainties and delayed perturbations. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 2003, 217(1), 1–5.
23.
ChenW.GuanZ.LuX.Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays. J. Franklin Inst., 2004, 341, 419–430.
24.
YuL.GaoF.Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays. J. Franklin Inst., 2001, 338, 101–110.
25.
JiangX.HanQ.Networked-induced delay-dependent H∞ controller design for a class of networked control systems. Asian J. Control, 2006, 8(2), 97–106.
26.
SongS.KimJ.YimC.KimH.H∞ control of discrete-time linear systems with time-varying delays in state. Automatica, 1999, 35(9), 1587–1591.
27.
FridmanE.ShakedU.Delay-dependent H∞ control of uncertain discrete delay systems. Eur. J. Control, 2005, 11(1), 29–37.
28.
BoydS.GhaouiL.FeronE.BalakrishnamV.Linear matrix inequalities in system and control, 1994 (SIAM, Philadelphia, Pennsylvania).
29.
XieL.SouzaC.Robust H∞ control for linear systems with norm-bounded time-varying uncertainty. IEEE Trans. Autom. Control, 1992, 37(8), 1188–1191.
30.
XieL.Output feedback H∞ control of systems with parameter uncertainty. Int. J. Control, 1996, 63(1), 741–750.
31.
GaoH.LamJ.WangC.Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Applic., 2004, 151(6), 691–698.
32.
GhaouiL.OustryF.A cone complementarity linearization algorithm for static output feedback and related problems. IEEE Trans. Autom. Control, 1997, 42(8), 1171–1176.
33.
ZhangX.WuM.SheJ.HanD.Delay dependent robust H∞ control for discrete time uncertain systems with time varying state delays. J. Control Theory Applic., 2006, 4(1), 355–360.
34.
LiuX.MartinR.WuM.TangM.Delay dependent robust stabilisation of discrete time systems with time varying delay. IEE Proc. Control Theory Applic., 2006, 153(6), 689–702.
35.
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 Control, 2008, 18(6), 630–647.
