This paper is concerned with the problem of observer design for a class of nonlinear systems with time-varying delay and bounded disturbances. For the stabilization problem, attention is focused on the design of a quantized observer that ensures stability of the closed-loop system. For the robust H∞ control problem, a quantized observer is designed such that, in addition to the requirement of the robust stability, a prescribed disturbance attenuation level also needs to be achieved. The nonlinearity is assumed to satisfy the local Lipschitz condition. A more general case is considered, differing from the previous results where the Lipschitz constant is fixed and predetermined. Finally, a numerical example is provided to show the effectiveness of our method.
AbbaszadehMMarquezH (2009) LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems. International Journal of Robust and Nonlinear Control19(3): 313-340.
2.
BalasubramaniamPNagamaniG (2012) A delay decomposition approach to delay-dependent robust passive control for Takagi-Sugeno fuzzy nonlinear systems. Circuits Systems and Signal Processing31(4): 1319-1341.
3.
BoydSVandenbergheL (2004) Convex Optimization. Cambridge: Cambridge University Press.
4.
ChangXYangG (2014) New results on output feedback H∞ control for linear discrete-time systems. IEEE Transactions on Automatic Control59(5): 1355-1359.
5.
ChenJ (2007) Robust H∞ output dynamic observer-based control of uncertain time-delay systems. Chaos, Solitons and Fractals31(2): 391-403.
6.
FanJZhangYZhengZ (2013) Observer-based reliable stabilization of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. ISA Transactions52(6): 730–737.
7.
FuMXieL (2005) The sector bound approach to quantized feedback control. IEEE Transactions on Automatic Control50(11): 1698-1711.
8.
GhanesMDe LeonJBarbotJ (2013) Observer design for nonlinear systems under unknown time-varying delays. IEEE Transactions on Automatic Control58(6): 1529-1534.
9.
HassanMAlrifaiMSolimanHet al. (2016) Observer-based controller for constrained uncertain stochas-tic nonlinear discrete-time systems. International Journal of Robust and Nonlinear Control26(10): 2090-2115.
10.
HoDLuG (2003) Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach. International Journal of Control76(2): 105-115.
11.
LiZLiuHGaoH (2011) A delay partitioning approach to H∞ filtering for continuous time-delay systems. Circuits Systems and Signal Processing30(3): 501-513.
12.
LienC (2004) Robust observer-based control of systems with state perturbations via LMI approach. IEEE Transactions on Automatic Control49(8): 1365-1370.
13.
LienC (2007) H∞ non-fragile observer-based controls of dynamical systems via LMI optimization approach. Chaos, Solitons and Fractals34(2): 428-436.
14.
LinCWangQLeeTet al. (2007) Observer-based H∞ control for fuzzy systems with time delay: Delaydependent design method. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics37(4): 1030-1038.
15.
LinCWangQLeeTet al. (2008) Design of observer-based H∞ control for fuzzy time-delay systems. IEEE Transactions on Fuzzy Systems16(2): 534-543.
16.
LinCWangZYangF (2009) Observer-based networked control for continuous-time systems with random sensor delays. Automatica45(2): 578-584.
17.
LiuHShenYZhaoX (2012) Delay-dependent observer-based H∞ finite-time control for switched systems with time-varying delay. Nonlinear Analysis: Hybrid Systems6(3): 885-898.
18.
LiuMYouJ (2012) Observer-based controller design for networked control systems with sensor quantisation and random communication delay. International Journal of Systems Science43(10): 1901-1912.
19.
LuRYangPBaiJet al. (2016) Quantized observer-based sliding mode control for networked control systems via the time-delay approach. Circuits Systems and Signal Processing35(5): 1563-1577.
20.
MeraMCastañosFPoznyakA (2014) Quantised and sampled output feedback for nonlinear systems. International Journal of Control87(12): 2475-2487.
21.
NaghshtabriziPHespanhaJ (2005) Designing an observer-based controller for a network control system. In: Proceedings of the 44th IEEE conference on decision and control, and the European control conference, Seville, Spain, 12–15 December 2005, pp. 848–853. IEEE.
22.
PetersenI (1987) A stabilization algorithm for a class of uncertain linear systems. Systems & Control Letters8(4): 351-357.
23.
SongJHeS (2014) Observer-based finite-time passive control for a class of uncertain time-delayed Lipschitz nonlinear systems. Transactions of the Institute of Measurement and Control36(6): 797-804.
24.
TanwaniAPrieurCFiacchiniM (2016) Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization. Systems & Control Letters94: 46-56.
25.
XuS (2002) Robust H∞ filtering for a class of discrete-time uncertain nonlinear systems with state delay. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications49(12): 1853-1859.
26.
XuSChenT (2002) Robust H∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control47(12): 2089-2094.
27.
ZhangLChenMSuH (2016) Observer-based semi-global consensus of discrete-time multi-agent systems with input saturation. Transactions of the Institute of Measurement and Control38(6): 665-674.
28.
ZhangJLamJXiaY (2011) Observer-based output feedback control for discrete systems with quantised inputs. IETControl Theory and Applications5(3): 478-485.
29.
ZhouB (2014) Observer-based output feedback control of discrete-time linear systems with input and output delays. International Journal of Control87(11): 2252-2272.
30.
ZhouBLiZLinZ (2013) Observer based output feedback control of linear systems with input and output delays. Automatica49(7): 2039-2052.
