In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.
BalasubramaniamPKrishnasamyRRakkiyappanP (2012) Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays. Communications Nonl. Sci. Numer. Simul. 17(9): 3612–3627.
2.
BoydSGhaouiLEFeronEBalakrishnanV (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM.
3.
ChaibiNTissirEH (2012) Delay dependent robust stability of singular systems with time-varying delay. International Journal of Automation and Computing, 10(1): 85–90.
4.
ChenJZhangTZhangZ, et al. (2018) Stability and output feedback control for singular Markovian jump delayed systems. Mathematical Control & Related Topics8(2): 475–490.
5.
ChengFHaoF (2013) Event-triggered control for linear descriptor systems. Circuits Syst. Signal Process32(3): 1065–1079.
6.
DaiL (1981) Singular Control Systems. Berlin: Springer.
7.
FridmanE (2002) Stability of linear descriptor system with delay: A Lyapunov based approach. J. Math. Analysis Appl., 273(1): 24–44.
8.
DuZYueDHuS (2014) stabilization for singular networked cascade control systems with state delay and disturbance. IEEE Trans. Indus. Inform., 10(2): 882–894.
9.
HaidarABoukasEK (2009) Exponential stability of singular systems with multiple time-varying delays. Automatica45: 539–545.
10.
HienLVVuLHPhatVN (2015) Improved delay-dependent exponential stability of singular systems with mixed interval time-varying delays. IET Contr. Theory Appl. 9(9): 1364–1372.
11.
KharitonovVL (2013) Time-Delay Systems Lyapunov. Functionals and Matrices. Berlin: Birkhauser.
12.
LiJSuHWuZChuJ (2012) Robust stabilization for discrete-time nonlinear singular systems with mixed time delays. Asian Journal of Control14(1): 1411–1421.
13.
LiuGWeiYMaQ, et al. (2017) Robust non-fragile guaranteed cost control for singular Markovian jump time-delay systems. Transactions of the Institute of Measurement and Control40(7): 2141–2150.
14.
LiuSZhouXFLiXJiangW (2017) Asymptotical stability of Riemann-Liouville fractional singular systems with multiple time-varying delays. Appl. Math. Lett. 65: 32–39.
15.
LiuYWangJGaoC, et al. (2016) On stability for discrete-time non-linear singular systems with switching actuators via average dwell time approach. Transactions of the Institute of Measurement and Control39(12): 1771–1776.
16.
LiuGMaQLuJ, et al. (2017) Mixed and passive filtering for a class of singular systems with interval time-varying delays. Optimal Control Applications and Methods39(1): 377–392.
17.
LongSZhongS (2017) control for a class of singular systems with state time-varying delay. ISA Transactions66: 10–21.
18.
MaritonM (1990) Jump Linear Systems in Automatic Control. Marcel Dekker, Inc
19.
NiamsupPPhatVN (2016) A new result on finite-time control of singular linear time-delay systems. Appl. Math. Letters60(1): 1–7.
20.
SauNHPhatVN (2018) LP approach to exponential stabilization of singular positive time-delay systems via memory state feedback. J. Indus. Manage. Optim. 14(2): 583–596.
21.
ShenYWuZGShiP, et al. (2019) control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica99: 352–360.
22.
ShuZLamJ (2010) Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays. International Journal of Control20(6): 1269–1284.
23.
XuSVan DoorenPStefanRLamJ (2002) Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control47(7): 1122–1128.
24.
WangHYingYLuRXueA (2016) Networked-based control for singular systems with event-triggered sampling scheme. Information Sciences329: 540–551.
25.
WangHZhouBLuRXueA (2014) New stability and stabilization criteria for a class of fuzzy singular systems with time-varying delay. Journal of The Franklin Institute351(7): 3766-3781.
26.
WeiJZhiHLiuK (2019) Stability and gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach. Transactions of the Institute of Measurement and Control41(15): 4197–4206.
27.
WuJLuGWoSXiaoX (2013) Exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays. International Journal of Robust Nonlinear Control23(12): 1393–1404.
28.
WuZGSuHShiPChuJ (2013) Analysis and Synthesis of Singular Systems with Time Delays. Berlin: Springer.
29.
YueDHanQL (2005) Delay-dependent robust controller design for uncertain descriptor systems with time-varying discrete and distributed delays. IET Control Theory and Applications152(6): 628–638.
30.
YueDHanQLPengC (2004) State feedback controller design of networked control systems. IEEE Transactions on Circuits and Systems II: Express Briefs51(11): 640–644.
31.
ZamaniIShafieeM (2015) Stability analysis of uncertain switched singular time-delay systems with discrete and distributed delays. Optimal Control Applications and Methods36(1): 1–28.
32.
ZhanTMaS (2019) Reduced-order observer design with unknown input for fractional-order descriptor nonlinear systems. Transactions of the Institute of Measurement and Control41(13): 3705–3713.
33.
ZhangWBranickyMSPhillipsSM (2001) Stability of networked control systems. IEEE Control Systems Magazine21(1): 8499–8505.
