Abstract
This paper investigates the problems of quantized \(H_{\infty }\) filtering for continuous-time nonhomogeneous Markov jump systems. The transition probability matrix is assumed to be time-varying and lies in a convex bounded domain. Firstly, we design the \(H_{\infty }\) filter with a mode-dependent logarithmic quantizer. Then based on the mode-dependent and parameter-dependent Lyapunov function, the stochastic stability with a prescribed \(H_{\infty }\) performance index is guaranteed by fully considering the information of time-varying transition probability. Specifically, stability criteria are established to make system stochastically stable and a cost function is given to satisfy the \(H_{\infty }\) performance. Finally, both numerical examples and practical example are given to illustrate the less conservatism and the feasibility of the proposed quantized filer design methods.
Similar content being viewed by others
References
S. Aberkane, Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems. Syst. Control Lett. 60(3), 156–160 (2011)
S. Aberkane, Bounded real lemma for nonhomogeneous Markovian jump linear systems. IEEE Trans. Autom. Control 58(3), 797–801 (2012)
E.K. Boukas, Stochastic Switching Systems: Analysis and Design (Springer Science & Business Media, Berlin, 2007)
E.K. Boukas, Z. Liu, Robust \(H_{\infty }\) control of discrete-time Markovian jump linear systems with mode-dependent time-delays. IEEE Trans. Autom. Control 46(12), 1918–1924 (2001)
X. Chen, Y. Wang, S. Hu, Event-triggered quantized \(H_{\infty }\) control for networked control systems in the presence of denial-of-service jamming attacks. Nonlinear Anal. Hybrid Syst. 33, 265–281 (2019)
Y. Ding, H. Liu, Stability analysis of continuous-time Markovian jump time-delay systems with time-varying transition rates. J. Frankl. Inst. 353(11), 2418–2430 (2016)
Y. Ding, H. Liu, K. Shi, \(H_{\infty }\) state-feedback controller design for continuous-time nonhomogeneous Markov jump systems. Optim. Control Appl. Methods 38(1), 133–144 (2017)
H. Dong, Z. Wang, H. Gao, On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays. Signal Process. 92(4), 1117–1125 (2012)
M. Fu, L. Xie, The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1698–1711 (2005)
H. Gao, T. Chen, \(H_{\infty }\) estimation for uncertain systems with limited communication capacity. IEEE Trans. Autom. Control 52(11), 2070–2084 (2007)
H. Gao, T. Chen, J. Lam, A new delay system approach to network-based control. Automatica 44(1), 39–52 (2008)
K. Han, X. Chang, Parameter-dependent robust \(H_{\infty }\) filter design for uncertain discrete-time systems with quantized measurements. Int. J. Control Autom. Syst. 11(1), 194–199 (2013)
K. Han, J. Feng, X. Chang, Reduced-order partially mode-dependent energy-to-peak filter design for discrete-time Markov jump systems subject to quantizer faults and state-dependent noises. Circuits Syst. Signal Process. 34(1), 77–103 (2015)
S. He, F. Liu, Robust peak-to-peak filtering for Markov jump systems. Signal Process. 90(2), 513–522 (2010)
X. He, Z. Wang, Y. Liu, L. Qin, D. Zhou, Fault tolerant control for an internet-based three-tank system: accommodation to sensor bias faults. IEEE Trans. Ind. Electron. 64(3), 2266–2275 (2016)
M. Hua, H. Tan, J. Chen, J. Fei, Robust delay-range-dependent non-fragile \(H_{\infty }\) filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays. J. Frankl. Inst. 352(3), 1318–1341 (2015)
M. Hua, L. Zhang, F. Yao, J. Ni, W. Dai, Y. Cheng, Robust \(H_{\infty }\) filtering for continuous-time nonhomogeneous Markov jump nonlinear systems with randomly occurring uncertainties. Signal Process. 148, 250–259 (2018)
M. Hua, D. Zheng, F. Deng, J. Fei, P. Cheng, X. Dai, \(H_{\infty }\) filtering for nonhomogeneous Markovian jump repeated scalar nonlinear systems with multiplicative noises and partially mode-dependent characterization. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2919146
Y. Kao, J. Xie, C. Wang, Stabilization of singular Markovian jump systems with generally uncertain transition rates. IEEE Trans. Autom. Control 59(9), 2604–2610 (2014)
J. Li, J.H. Park, Fault detection filter design for switched systems with quantization effects. J. Frankl. Inst. 353(11), 2431–2450 (2016)
H. Liu, Y. Ding, J. Cheng, New results on \(H_{\infty }\) filtering for Markov jump systems with uncertain transition rates. ISA Trans. 69, 43–50 (2017)
H. Liu, D.W.C. Ho, F. Sun, Design of \(H_{\infty }\) filter for Markov jumping linear systems with non-accessible mode information. Automatica 44(10), 2655–2660 (2008)
R. Lu, H. Li, Y. Zhu, Quantized \(H_{\infty }\) filtering for singular time-varying delay systems with unreliable communication channel. Circuits Syst. Signal Process. 31(2), 521–538 (2012)
S. Ma, E.K. Boukas, Y. Chinniah, Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay. Int. J. Robust Nonlinear Control 20(5), 531–543 (2010)
I.R. Petersen, A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8(4), 351–357 (1987)
R. Rakkiyappan, K. Maheswari, G. Velmurugan, J.H. Park, Event-triggered \(H_{\infty }\) state estimation for semi-Markov jumping discrete-time neural networks with quantization. Neural Netw. 105, 236–248 (2018)
H. Shen, S. Huo, H. Yan, J.H. Park, V. Sreeram, Distributed dissipative state estimation for Markov jump genetic regulatory networks subject to round-robin scheduling. IEEE Trans. Neural Netw. Learn. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2909747
H. Shen, Y. Men, J. Cao, J.H. Park, \(H_{\infty }\) filtering for fuzzy jumping genetic regulatory networks with round-robin protocol: a hidden-Markov-model-based approach. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2939965
M. Shen, J.H. Park, \(H_{\infty }\) filtering of Markov jump linear systems with general transition probabilities and output quantization. ISA Trans. 63, 204–210 (2016)
M. Shen, J.H. Park, D. Ye, A separated approach to control of Markov jump nonlinear systems with general transition probabilities. IEEE Trans. Cybern. 46(9), 2010–2018 (2016)
H. Shen, L. Su, Z. Wu, J.H. Park, Reliable dissipative control for Markov jump systems using an event-triggered sampling information scheme. Nonlinear Anal. Hybrid Syst. 25, 41–59 (2017)
H. Shen, Z. Wu, J.H. Park, Reliable mixed passive and \(H_{\infty }\) filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. Int. J. Robust Nonlinear Control 25(17), 3231–3251 (2015)
Y. Shen, Z. Wu, P. Shi, Z. Shu, H.R. Karimi, \(H_{\infty }\) control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica 99, 352–360 (2019)
M. Shen, D. Ye, Q. Wang, Event-triggered \(H_{\infty }\) filtering of Markov jump systems with general transition probabilities. Inf. Sci. 418–419, 635–651 (2017)
Y. Shi, B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)
C.E. Souza, A. Trofino, K.A. Barbosa, Mode-independent \(H_{\infty }\) filters for Markovian jump linear systems. IEEE Trans. Autom. Control 51(11), 1837–1841 (2006)
G. Wang, H. Bo, Q. Zhang, \(H_{\infty }\) filtering for time-delayed singular Markovian jump systems with time-varying switching: a quantized method. Signal Process. 109, 14–24 (2015)
H. Wang, P. Shi, R.K. Agarwal, Network-based event-triggered filtering for Markovian jump systems. Int. J. Control 89(6), 1096–1110 (2016)
G. Wang, P. Zhang, Q. Zhang, A generalized robust \(H_{\infty }\) filtering for singular Markovian jump systems and its applications. Int. J. Robust Nonlinear Control 24(18), 3491–3507 (2014)
Y. Wei, J. Qiu, H.R. Karimi, Quantized \(H_{\infty }\) filtering for continuous-time Markovian jump systems with deficient mode information. Asian J. Control 17(5), 1914–1923 (2015)
Z. Wu, P. Shi, H. Su, J. Chu, Asynchronous \(l_2\)-\(l_{\infty }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica 50(1), 180–186 (2014)
J. Xiong, J. Lam, H. Gao, D.W.C. Ho, On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41(5), 897–903 (2005)
D. Yao, R. Lu, Y. Xu, L. Wang, Robust \(H_{\infty }\) filtering for Markov jump systems with mode-dependent quantized output and partly unknown transition probabilities. Signal Process. 137, 328–338 (2017)
X. Yao, L. Wu, W. Zheng, Quantized \(H_{\infty }\) filtering for Markovian jump LPV systems with intermittent measurements. Int. J. Robust Nonlinear Control 23(1), 1–14 (2013)
Y. Yin, P. Shi, F. Liu, K.L. Teo, Filtering for discrete-time nonhomogeneous Markov jump systems with uncertainties. Inf. Sci. 259, 118–127 (2014)
Y. Yin, P. Shi, F. Liu, K.L. Teo, C.C. Lim, Robust filtering for nonlinear nonhomogeneous Markov jump systems by fuzzy approximation approach. IEEE Trans. Cybern. 45(9), 1706–1716 (2015)
L. Zhang, E.K. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2), 463–468 (2009)
L. Zhang, E.K. Boukas, Mode-dependent \(H_{\infty }\) filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(6), 1462–1467 (2009)
M. Zhang, P. Shi, L. Ma, J. Cai, H. Su, Quantized feedback control of fuzzy Markov jump systems. IEEE Trans. Cybern. 49(9), 3375–3384 (2018)
J. Zhang, W. Sun, Z. Feng, Vehicle yaw stability control via \(H_\infty \) gain scheduling. Mech. Syst. Signal Process. 106, 62–75 (2018)
Acknowledgements
The authors thank the editor and the reviewers for their constructive comments and suggestions to improve the manuscript. This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20181157, the Fundamental Research Funds for the Central Universities under Grant 2019B22114 and Qing Lan Project (Grant Szx/16A205).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hua, M., Bian, C., Chen, J. et al. Quantized \(H_{\infty }\) Filtering for Continuous-Time Nonhomogeneous Markov Jump Systems. Circuits Syst Signal Process 39, 3833–3857 (2020). https://doi.org/10.1007/s00034-020-01343-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-020-01343-8