This paper addresses the problem of stability and stabilization for a class of two-dimensional (2-D) Roesser systems with time-varying delays subject to missing measurements. The missing phenomenon of the sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution. The aim of this paper is focused on the design of a state feedback controller such that the closed-loop 2-D system is asymptotic stability in the mean square sense. A delay-dependent stability condition is derived in terms of linear matrix inequalities, and formulas can be given for the control law design. Furthermore, the results are also extended to robust stability and stabilization of the uncertain 2-D time-varying delayed system. Numerical examples are given to illustrate the effectiveness of proposed approach.
AhnCWuLGShiP (2016) Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica69: 356–363.
2.
BoydSGhaouiLEFeronEBalakrishnanV (1994) Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, PA: SIAM.
3.
BuXHWangHQHouZSQianW (2014a) H∞ control for a class of 2-d nonlinear systems with intermittent measurements. Applied Mathematics and Computation247: 51–662.
4.
BuXHWangHQHouZSQianW (2014b) Stabilisation of a class of two-dimensional nonlinear systems with intermittent measurements. IET Control Theory & Application8(15): 1596–1604.
5.
ChenSF (2010a) Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model. Applied Mathematics and Computation216 (9): 2613–2622.
6.
ChenSF (2010b) Stability analysis for 2-D systems with interval time-varying delays and saturation nonlinearities. Signal Process90(7): 2265–2275.
7.
DuCXieL (1999) Stability analysis and stabilization of uncertain two-dimensional discrete systems: An LMI approach. IEEE Transactions on, Circuits and Systems I: Fundamental Theory and Applications46(11): 1371–1374.
8.
DuCXieLZhangC (2001) H∞ and robust stabilization of two-dimensional systems in Roesser models. Automatica37(2): 205–211.
9.
FanHWenC (2003) Adaptive control of a class of 2-D discrete systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications I50(1): 166–172.
10.
FengZYXuLWuMHeY (2010) Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays. IET Control Theory & Applications4(10): 1959–1971.
11.
GaoHLamJXuSWangC (2005) Stability and stabilization of uncertain 2-D discrete systems with stochastic perturbation. Multidimensional Systems and Signal Processing16(1): 85–106.
12.
GhaouiELOustryFAitramiM (1997) A cone complementarity linearization algorithms for static output feedback and related problems. IEEE Transactions on Automation Control42(8): 1171–1176.
13.
GhousIXiangZR (2015a) Hinf stabilization of 2-D discrete switched delayed systems represented by the Roesser model subject to actuator saturation. Transactions of the Institute of Measurement and Control37(10): 1242–1253.
14.
GhousIXiangZR (2015b) Hinf control of 2-D continuous nonlinear systems with time varying delays. Journal of the Franklin Institute352(12): 5758–5778.
15.
GuanXLongCDuanG (2001) Robust optimal guaranteed cost control for 2-d discrete systems. IEE Proceedings on Control Theory and Applications48(5): 1355–361.
16.
HespanhaJPNaghshtabriziPXuYG (2007) A survey of recent results in networked control systems. Proceedings of the IEEE95(1): 138–162.
17.
HuangSPXiangZR (2016) Stability analysis of two-dimensional switched non-linear continuous-time systems. IET Control Theory & Applications10(6): 724–729.
18.
KaczorekT (1985) Two-Dimensional Linear Systems. Berlin: Springer-Verlag.
19.
LiangJLWangZDWangYRLiuXH (2014) State estimation for two-dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays. International Journal of Robust and Nonlinear Control24(1): 18–38.
20.
LiangJWangZLiuXH (2015) H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements. Journal of the Franklin Institute352(3): 1007–1030.
21.
LiuDMichelAN (1994) Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications41(2): 127–137.
22.
LiuXGaoHShiP (2009) Robust H∞ filtering for 2-d systems with intermittent measurements. Circuits, Systems & Signal Processing28(2): 283–303.
23.
MoonYSParkPKwonWHLeeYS (2001) Delay-dependent robust stabilisation of uncertain state delayed systems. International Journal of Control74(14): 1447–1455.
24.
PaszkeWLamJGalkowskiK.et al. (2004) Robust stability and stabilisation of 2D discrete state- delayed systems. Systems & Control Letters51(3–4): 277–291.
25.
PengDGuanX (2009) H∞ filtering of 2-D discrete state delayed systems. Multidimensional Systems and Signal Processing20(3): 265–274.
26.
QiuJXiaYYangHZhangJ (2008) Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators. IET Control Theory Application2(1): 87–93.
27.
ShiJGaoFWuT-J (2005) Robust design of integrated feedback and iterative learning control of a batch process based on a 2-D Roesser system. Journal of Process Control15(8): 907–924.
28.
SinghV (2008) Stability Analysis of 2-D discrete systems described by the fornasini-marchesini second model with state saturation. IEEE Transactions on Circuits and Systems II: Express Briefs55(8): 793–796.
29.
SinghV (2012) New approach to stability of 2-D discrete systems with state saturation. Signal Processing92(1): 240–247.
30.
WangLMMoSYZhouDHGaoFR (2011) Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays. Journal of Process Control21(7): 987–996.
31.
WangYYangYZhaoZ (2013) Robust stability analysis for an enhanced ILC-based PI controller. Journal of Process Control23(2): 201–214.
32.
WeissNA (2005) A Course in Probability. Boston: Addison–Wesley, pp. 380–383.
33.
WuLGaoH (2008) Sliding mode control of two-dimensional systems in Roesser model. IET Control Theory & Applications2(4): 352–364.
34.
XuJMYuL (2009) Delay-dependent H∞ control for 2-D discrete state delay systems in the second FM model. Multidimensional Systems and Signal Processing20(4): 333–349.
35.
YangTC (2006) Networked control system: A brief survey. IEE Proceedings-Control Theory and Applications153(4): 403–412.
36.
YeSWangW (2011) Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems. International Journal of Systems Science42(5): 839–851.
37.
ZhangWBranickyMSPhillipsSM (2001) Stability of networked control systems. IEEE Control Systems Magazine21(1): 85–99.
