This paper investigates the problem of robust H∞ filtering for switched discrete-time systems with missing measurements and asynchronous switching. The missing measurements are modelled as a binary switch sequence specified by a conditional probability distribution. The purpose of the paper is the design of a filter such that for all admissible uncertainties, the error system is exponentially mean square stable, and the norm of the transfer function, from the noise signal to the estimation error, is below a pre-specified level. By using the average dwell time approach, a sufficient condition for the existence of such a filter is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.
ChengDGuoLLinYWangY (2005) Stabilization of switched linear systems. IEEE Transactions on Automatic Control50(5): 661–666.
2.
HespanhaJPMorseAS (1999) Stability of switched systems with average dwell time. Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, pp. 2655–2660.
3.
HounkpeviFOYazEE (2007) Robust minimum variance linear state estimators for multiple sensors with different failure rates. Automatica43(7): 1274–1280.
4.
JiZGuoXXuSWangL (2007) Stabilization of switched linear systems with time-varying delay in switching occurrence detection. Circuits, Systems and Signal Processing26(3): 361–367.
5.
LiberzonDHespanhaJPMorseAS (1999) Stability of switched systems: a Lie-algebraic condition. Systems and Control Letters37(3): 117–122.
6.
MahmoudMS (2008) Delay-dependent H∞ filtering of a class of switched discrete-time state delay systems. Signal Processing88(11): 2709–2719.
7.
NahiN (1969) Optimal recursive estimation with uncertain observation. IEEE Transactions on Information Theory15(4): 457–462.
8.
OobaTFunahashiY (1997) On a common quadratic Lyapunov function for widely distant systems. IEEE Transactions on Automatic Control42(12): 1697–1699.
9.
SinopoliBSchenatoLFranceschettiMPoollaKJordanMISastrySS (2004) Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control49(9): 1453–1464.
10.
SubramanianASayedAH (2004) Multiobjective filter design for uncertain stochastic time-delay systems. IEEE Transactions on Automatic Control49(1): 149–154.
11.
SunZGeSS (2005) Analysis and synthesis of switched linear control systems. Automatica41(2): 181–195.
12.
WangWYangFW (2006) H∞ filtering design for discrete-time systems with missing measurements. Acta Automatica Sinica32(1): 107–111.
13.
WangZYangFHoDWCLiuX (2006) Robust H∞ filtering for stochastic time-delay systems with missing measurements. IEEE Transactions on Signal Processing54(7): 2579–2587.
14.
WuLHoDWC (2009) Reduced-order L2−L∞ filtering for a class of nonlinear switched stochastic systems. IET Control Theory and Applications3(5): 493–508.
15.
XiaYLiuGPShiPReesDThomasEJC (2007) New stability and stabilization conditions for systems with time-delay. International Journal of Systems Science38(1): 17–24.
16.
XiaYShangJChenJLiuGP (2009) Networked data fusion with packet losses and variable delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics39(5): 1107–1120.
17.
XiangWXiaoJ (2011) H∞ filtering for switched nonlinear systems under asynchronous switching. International Journal of Systems Science42(5): 751–765.
18.
XiangZLiangCChenQ (2011) Robust L2−L∞ filtering for switched systems under asynchronous switching. Communications in Nonlinear Science and Numerical Simulation16(8): 3303–3318.
19.
XiangZRWangRH (2009a) Robust control for uncertain switched non-linear systems with time delay under asynchronous switching. IET Control Theory and Applications3(8): 1041–1050.
20.
XiangZRWangRH (2009b) Robust stabilization of switched non-linear systems with time-varying delays under asynchronous switching. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering223(8): 1111–1128.
21.
XieL (1996) Output feedback H∞ control of systems with parameter uncertainty. International Journal of Control63(4): 741–750.
22.
YangHXiaYQiuJZhangJ (2010) Filtering for a class of discrete-time systems with time-delays via delta operator approach. International Journal of Systems Science41(4): 423–433.
23.
ZhaiGHuBYasudaKMichelAN (2001) Disturbance attenuation properties of time-controlled switched systems. Journal of the Franklin Institute338(7): 765–779.
24.
ZhangHChenQJYanHCLiuJH (2009) Robust H∞ filtering for switched stochastic system with missing measurements. IEEE Transactions on Signal Processing57(9): 3466–3474.
25.
ZhangLGaoH (2010) Asynchronously switched control of switched linear systems with average dwell time. Automatica46(5): 953–958.
26.
ZhangLShiP (2009) Stability, L2-gain and asynchronous control of discrete-time switched systems with average dwell time. IEEE Transactions on Automatic Control54(9): 2193–2200.
27.
ZhangLCuiNLiuMZhaoY (2011) Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Transactions on Circuits and Systems I: Regular Papers58(5): 1109–1118.
28.
ZhangLShiPWangCGaoH (2006) Robust H∞ filtering for switched linear discrete-time systems with polytopic uncertainties. International Journal of Adaptive Control and Signal Processing20(6): 291–304.
29.
ZhangWBranickyMSPhillipsSM (2001) Stability of networked control systems. IEEE Control Systems Magazine21(1): 84–99.
30.
ZongGDHouLLLiJF (2011a) A descriptor system approach to l2−l∞ filtering for uncertain discrete-time switched system with mode-dependent time-varying delays. International Journal of Innovative Computing, Information and Control7(5A): 2213–2224.
31.
ZongGDHouLLXuSY (2010) Robust l2−l∞ state feedback control for uncertain discrete-time switched systems with mode-dependent time-varying delay. Asian Journal of Control12(4): 568–573.
32.
ZongGDHouLLWuYQ (2011b) Exponential l2−l∞ filtering for discrete-time switched systems under a new framework. International Journal of Adaptive Control and Signal Processing, DOI: 10.1002/acs.1280.
33.
ZongGDHouLLWuYQ (2011c) Robust l2−l∞ guaranteed cost filtering for uncertain discrete-time switched system with mode-dependent time-varying delays. Circuits, Systems, and Signal Processing30(1): 17–33.
