The problem of finite-time filtering for nonlinear Markovian jump systems subject to extended dissipativity with unknown transition rates and time-varying delays is investigated in this paper. Firstly, by constructing novel Lyapunov-Krasovskii functionals and utilizing delay partitioning method, the error system is proved to be stochastically finite-time bounded and extended dissipative. Secondly, in virtue of linear matrix inequalities approach, the desired mode-dependent filter is obtained. Finally, two simulations are illustrated for the purpose of demonstrating the less conservativeness and effectiveness of the proposed method.
AkbariNSadrAKazemyA (2019) Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay. Transactions of the Institute of Measurement and Control41(9): 2535–2544.
2.
AmatoFAriolaMDoratoP (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica37(9): 1459–1463.
3.
BrogliatoBLozanoRMaschkeBEgelandO (2007) Dissipative Systems Analysis and Control. Berlin: Springer.
4.
ChengJHuangWLamHK, et al. (2020) Fuzzy-model-based control for singularly perturbed systems with nonhomogeneous Markov switching: A dropout compensation strategy. IEEE Transactions on Fuzzy Systems. DOI:10.1109/TFUZZ.2020. 3041588.
5.
ChengJParkJHZhaoX, et al. (2019) Quantized nonstationary filtering of networked Markov switching RSNSs: A multiple hierarchical structure strategy. IEEE Transactions on Automatic Control65(11): 4816–4823.
6.
ChengJShanYCaoJParkJH (2021) Nonstationary control for T-S fuzzy Markovian switching systems with variable quantization density. IEEE Transactions on Fuzzy Systems29(6): 1375–1385.
7.
CostaOFragosoMTodorovM (2013) Continuous-time Markov Jump Linear Systems. Berlin: Springer.
8.
CuiGYuJWangQ (2020) Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping. IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access). DOI:10.1109/TSMC.2020.3010642.
9.
DaiMXiaJParkJH, et al. (2019) Asynchronous dissipative filtering for Markov jump discrete-time systems subject to randomly occurring distributed delays. Journal of the Franklin Institute356(4): 2395–2420.
10.
ElsayedAGrimbleM (1989) A new approach to the design of optimal digital linear filters. IMA Journal of Mathematical Control and Information6(2): 233–251.
11.
FengZLamJ (2013) Reliable dissipative control for singular Markovian systems. Asian Journal of Control15(3): 901–910.
12.
GrayWSGonzálezORDoganM (2000) Stability analysis of digital linear flight controllers subject to electromagnetic disturbances. IEEE Transactions on Aerospace and Electronic Systems36(4): 1204–1218.
13.
GrigoriiadisKWatsonJ (1997) Reduced order and filtering via linear matrix inequaties. IEEE Transactions on Aerospace and Electronic Systems33(4): 1326–1338.
14.
HouLZongGZhengWWuY (2013) Exponential control for discrete-time switching Markov jump linear systems. Circuits, Systems, and Signal Processing32(6): 2745–2759.
15.
LiHShiPYaoD (2016) Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults. IEEE Transactions on Automatic Control62(4): 1933–1939.
16.
LiJHuangXLiZ (2017) Extended dissipative filtering of fuzzy systems with time-varying delay under imperfect premise matching. International Journal of Systems Science48(8): 1731–1743.
17.
LiJShenLYaoFZhaoHWangJ (2018) An event-triggered approach to finite-time observer-based control for Markov jump systems with repeated scalar nonlinearities. Transactions of the Institute of Measurement and Control40(9): 2789–2797.
18.
LiLShiPAhnCK (2020) Distributed iterative FIR consensus filter for multiagent systems over sensor networks. IEEE Transactions on Cybernetics. DOI:10.1109/TCYB.2020.3035866.
19.
LiLUgrinovskiiVAOrsiR (2007) Decentralized robust control of uncertain Markov jump parameter systems via output feedback. Automatica43(11): 1932–1944.
20.
LiuGParkJHXuSZhuangG (2019) Robust non-fragile fault detection filter design for delayed singular Markovian jump systems with linear fractional parametric uncertainties. Nonlinear Analysis: Hybrid Systems32: 65–78.
21.
MaoX (2002) Exponential stability of stochastic delay interval Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with timevarying delays systems with Markovian switching. IEEE Transactions on Automatic Control47(10): 1604–1612.
22.
NiculescuSLozanoR (2001) On the passivity of linear delay systems. IEEE Transactions on Automatic Control46(3): 460–464.
23.
PeaucelleDArzelierDHenrionDGouaisbautF (2007) Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation. Automatica43(5): 795–804.
24.
SeuretAGouaisbautF (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica49(9): 2860–2866.
25.
SuXShiPWuLBasinMV (2014) Reliable filtering with strict dissipativity for T-S fuzzy time-delay systems. IEEE Transactions on Cybernetics44(12): 2470–2483.
26.
TaoJWuZSuH, et al. (2018) Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity. IEEE Transactions on Cybernetics49(7): 2504–2513.
27.
TsiotrasP (1998) Further passivity results for the attitude control problem. IEEE Transactions on Automatic Control43(11): 1597–1600.
28.
WangJLuoY (2008) Further improvement of delay-dependent stability for Markov jump systems with time-varying delay. In: 2008 7th World Congress on Intelligent Control and Automation, 25–27 June, pp. 6319–6324. Chongqing, China: IEEE.
29.
WangYXuSLuJZhangZ (2021) Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays. Nonlinear Dynamics104: 509–521.
30.
WangYZhuangGChenF (2019) Event-based asynchronous dissipative filtering for T-S fuzzy singular Markovian jump systems with redundant channels. Nonlinear Analysis: Hybrid Systems34: 264–283.
31.
WillemsJC (1972) Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis45(5): 321–351.
32.
WuZParkJHSuHChuJ (2013a) Delay-dependent passivity for singular Markov jump systems with time-delays. Communications in Nonlinear Science and Numerical Simulation18(3): 669–681.
33.
WuZParkJHSuH, et al. (2013b) Mixed and passive filtering for singular systems with time delays. Signal Processing93(7): 1705–1711.
34.
XieLde SouzaCE (1992) Robust control for linear systems with norm bounded time-varying uncertainty. IEEE Transactions on Automatic Control37(8): 1188–1191.
35.
XuNSunL (2019) Synchronization control of Markov jump neural networks with mixed time-varying delay and parameter uncertain based on sample point controller. Nonlinear Dynamics98: 1877–1890.
36.
XuSLamJ (2006) Robust Control and Filtering of Singular Systems. Berlin: Springer.
37.
XuSLamJMaoX (2007) Delay-dependent control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers54(9): 2070–2077.
38.
XuSLamJZouY (2003) filtering for singular systems. IEEE Transactions on Automatic Control48(12): 2217–2222.
39.
YangGKaoYJiangBYinJ (2017) Delay-dependent filtering for singular Markovian jump systems with general uncomplete transition probabilities. Applied Mathematics and Computation294: 195–215.
40.
YaoDLuRXuYWangL (2017) Robust filtering for Markov jump systems with mode-dependent quantized output and partly unknown transition probabilities. Signal Processing137: 328–338.
41.
YinYShiPLiuFTeoKL (2015) Robust filtering for a class of dynamical systems with nonhomogeneous Markov jump process. International Journal of Systems Science46(4): 599–608.
42.
ZhangBZhengWXuS (2013) Filtering of Markovian jump delay systems based on a new performance index. IEEE Transactions on Circuits and Systems I: Regular Papers60(5): 1250–1263.
43.
ZhaoXZengQ (2010) Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays. International Journal of Automation and Computing7(2): 224–229.
44.
ZhuangGLuJZhangM (2014) Robust filter design for uncertain stochastic Markovian jump Hopfield neural networks with mode-dependent time-varying delays. Neurocomputing127: 181–189.
45.
ZhuangGSuSXiaJSunW (2020a) HMM-based asynchronous filtering for fuzzy singular Markovian switching systems with retarded time-varying delays. IEEE Transactions on Cybernetics (Early Access). DOI: 10.1109/TCYB.2020.2977127.
46.
ZhuangGSunWSuSXiaJ (2020b) Asynchronous feedback control for delayed fuzzy degenerate jump systems under observer-based event-driven characteristic. IEEE Transactions on Fuzzy Systems (Early Access). DOI: 10.1109/TFUZZ.2020. 3027336.
47.
ZhuangGXiaJFengJSunWZhangB (2020c) Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat’s lemma. IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access). DOI: 10.1109/TSMC.2020. 2964057.
48.
ZongGLiYHouLSunH (2016) Disturbance-observer-based-control and resilient control for Markovian jump nonlinear systems with multiple disturbances and its application to single robot arm system. IET Control Theory Application10(2): 226–233.
49.
ZongGYangDHouLWangQ (2013) Robust finite-time control for Markovian jump systems with partially known transition probabilities. Journal of the Franklin Institute350(6): 1562–1578.
