This article investigates the robust guaranteed cost H∞ control problem for a class of singular systems with multiple time delays subject to input saturation. The delay-dependent sufficient condition and the robust guaranteed cost H∞ controller are proposed which guarantee that the closed-loop system is regular, impulse free and stable via Lyapunov theory, singular value theory and linear matrix inequality approach. A guaranteed cost function for the closed-loop systems has an upper bound irrespective of all admissible parameter uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.
HaleJKVerduvn LunelSM. Introduction to functional differential equations. New York: Springer Verlag, 1993.
2.
LuRQSuHY. Robust stability theory of singular systems. Beijing: Science Publishers, 2008.
3.
XuSLamJ. Robust control and filtering of singular systems. Berlin: Springer, 2006.
4.
YangFZhangQL. Delay-dependent H∞ control of linear descriptor systems with delay in state. J Contr Theor Appl2005; 3(1): 76–84.
5.
MaYCGuNNZhangQL. Non-fragile robust H control for uncertain discrete-time singular systems with time-varying delays. J Franklin Inst2014; 351(6): 3163–3181.
6.
LiHYGaoHJShiP. New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans Neural Network2010; 21(11): 1842–1847.
7.
LiHYJingXJKarimiHR. Output-feedback-based H∞ control for vehicle suspension systems with control delay. IEEE Trans Ind Electron2014; 61(1): 436–446.
8.
LiHYLiuHHGaoHJ. Reliable fuzzy control for active suspension systems with actuator delay and fault. IEEE Trans Fuzzy Syst2012; 20(2): 342–357.
9.
JiangZHGuiWHXieYF. Memory state feedback control for singular systems with multiple internal incommensurate constant point delays. Acta Automat Sinica2009; 35(2): 174–179.
10.
MaYCYangBZhangZJ. H∞ control for multi-time-delay uncertain discrete systems. Int J Innov Comput I2010; 6(5): 2035–2044.
11.
FangM. Delay-dependent robust H∞ control for uncertain singular systems with state delay. Acta Automat Sinica2009; 35(1): 65–70.
12.
FengYZhuXZhangQ. An improved stabilization condition for singular time-delay systems. Int J Innov Comput I2010; 6(5): 2025–2034.
13.
LongSHZhongSMLiuZJ. H∞ filtering for a class of singular Markovian jump systems with time-varying delay. Signal Process2012; 92(11): 2759–2768.
14.
LiuLLPengJGWuBW. H∞ control of singular time-delay systems via discretized Lyapunov functional. J Franklin Inst2011; 348(4): 749–762.
15.
LiHYYuJYHiltonC. Adaptive sliding mode control for nonlinear active suspension systems using T-S fuzzy model. IEEE Trans Ind Electron2013; 60(8): 3328–3338.
16.
LiHYGaoHJShiP. Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach. Automatica2014; 50(7): 1825–1834.
17.
MaYCHuangLFZhangQL. Robust guaranteed cost H∞ control for uncertain time-varying delay system. Acta Phys Sinica2007; 56(7): 3744–3752.
18.
ShiGDWoSLZouY. Guaranteed cost control for singular systems with time-delay and parameter uncertainty. Syst Eng and Electron2006; 28(2): 266–270.
19.
WoSLShiGDZouY. Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty. J Syst Eng Electron2007; 18(1): 111–119.
20.
ChenJWangXPDingRF. Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities. Appl Math Model2012; 36(1): 238–243.
21.
ZhangLXBoukasEKHaidarA. Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica2008; 44: 2691–2695.
22.
WangXAliSAntonAS. Simultaneous global external and internal stabilization of linear time-invariant discrete-time systems subject to actuator saturation. Automatica2012; 48(5): 699–711.
23.
LuFCXiaYQFuMY. Controller design for rigid spacecraft attitude tracking with actuator saturation. Inform Sci2013; 220: 343–366.
24.
ZuoZQHoDWCWangWJ. Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation. Automatica2010; 46(3): 569–576.
25.
MaSPZhangCH. H∞ control for discrete-time singular Markov jump systems subject to actuator saturation. J Franklin Inst2012; 349(3): 1011–1029.
26.
HaidarABoukasBKXuS. Exponential stability and static output feedback stabilization of singular time-delay systems with saturating actuators. IET Control Theory A2009; 3(9): 1293–1305.
27.
YangCYSunJMaXP. Stabilization bound of singularly perturbed systems subject to actuator saturation. Automatica2013; 49: 457–462.
28.
LinZLvL. Set invariance conditions for singular linear systems subject to actuator saturation. IEEE Trans Automat Contr2007; 52(12): 2351–2355.
29.
LvLLinZ. Analysis and design of singular linear systems under actuator saturation and L2/L1 disturbances. Syst Contr Lett2008; 57: 904–912.
30.
XuYNMaYCShiJX. Robust guaranteed cost H∞ control for time-delay singular systems with input saturation. In: Chinese control and decision conference, Guilin, China, 17–19 June 2009, pp.1427–1431. New York: IEEE.
31.
FridmanE. Stability of linear descriptor systems with delay: a Lyapunov-based approach. J Math Anal Appl2002; 273(1): 24–44.
32.
FridmanEShakedU. H∞ control of linear state-delay descriptor systems: an LMI approach. Lin Algebra Appl2002; 351(1): 271–302.
