Fault detection filter design for continuous-time nonlinear Markovian jump systems with mode-dependent delay and time-varying transition probabilities
Tóm tắt
This paper focuses on fault detection filter (FDF) design for continuous-time nonlinear Markovian jump systems (NMJSs) with mode-dependent delay and time-varying transition probabilities (TPs). By using a novel Lyapunov-Krasovskii function and based on convex polyhedron technique, a new FDF, as the residual generator, is constructed to guarantee the mean-square exponential stability and a prescribed level of disturbance attenuation for admissible perturbations of NMJSs. Finally, the numerical simulation is carried out to demonstrate the effectiveness of our method.
Tài liệu tham khảo
Mao, X: Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 47(10), 1604-1612 (2002)
Wang, B, Cheng, J, Al-Barakati, A, Fardoun, H: A mismatched membership function approach to sampled-data stabilization for T-S fuzzy systems with time-varying delayed signals. Signal Process. 140, 161-170 (2017)
Fan, HJ, Liu, B, Wang, W, Wen, CY: Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises. Automatica 51, 200-209 (2015)
Zhang, L, Boukas, EK: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2), 463-468 (2009)
Wang, B, Yan, J, Cheng, J, Zhong, SM: New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals. Appl. Math. Comput. 314, 322-333 (2017)
Wang, Z, Liu, Y, Liu, X: Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656-1662 (2010)
Wang, B, Shi, P, Karimi, HR: Fuzzy sliding mode control design for a class of disturbed systems. J. Franklin Inst. 351(7), 3593-3609 (2014)
Zhao, H, Chen, Q, Xu, S: \(H_{\infty}\) guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays. J. Franklin Inst. 346(10), 945-957 (2009)
Cheng, J, Wang, B, Park, JH, Kang, W: Sampled-data reliable control for T-S fuzzy semi-Markovian jump system and its application to single-link robot arm model. IET Control Theory Appl. 11(12), 1904-1912 (2017)
Wang, B, Shi, P, Karimi, HR, Song, Y, Wang, J: Robust \(H_{\infty}\) synchronization of a hyper-chaotic system with disturbance input. Nonlinear Anal., Real World Appl. 14(3), 1487-1495 (2013)
Cheng, J, Park, JH, Liu, Y, Liu, Z, Tang, L: Finite-time \(H_{\infty}\) fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions. Fuzzy Sets Syst. 314, 99-115 (2017)
Wang, B, Cheng, J, Zhan, J: A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays. Nonlinear Anal. Hybrid Syst. 26, 239-253 (2017)
Cheng, J, Park, JH, Karimi, HR, Zhao, X: Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays. Inf. Sci. 399, 219-238 (2017)
Wu, Z, Su, H, Chu, J: \(H_{\infty}\) filtering for singular Markovian jump systems with time delay. Int. J. Robust Nonlinear Control 20(8), 939-957 (2010)
Liu, J, Gu, Z, Hu, S: \(H_{\infty}\) filtering for Markovian jump systems with time-varying delays. Int. J. Innov. Comput. Inf. Control 7(3), 1299-1310 (2011)
Shen, H, Xu, S, Song, X, Chu, Y: Delay-dependent \(H_{\infty}\) filtering for stochastic systems with Markovian switching and mixed mode-dependent delays. Nonlinear Anal. Hybrid Syst. 4(1), 122-133 (2010)
Karimi, HR, Zapateiro, M, Luo, N: A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations. J. Franklin Inst. 347(6), 957-973 (2010)
Liu, M, Shi, P, Zhang, L, Zhao, X: Fault-tolerant control for nonlinear Markovian jump systems via proportional and derivative sliding mode observer technique. IEEE Trans. Circuits Syst. I 58(11), 2755-2764 (2011)
Zhong, M, Ding, Q, Shi, P: Parity space-based fault detection for Markovian jump systems. Int. J. Syst. Sci. 40(4), 421-428 (2009)
Wang, H, Wang, C, Gao, H, Wu, L: An LMI approach to fault detection and isolation filter design for Markovian jump system with mode-dependent time-delays. In: Proceedings of the American Control Conference, Minneapolis, USA, pp. 5686-5691 (2006)
Yao, X, Wu, L, Zheng, WX: Fault detection filter design for Markovian jump singular systems with intermittent measurements. IEEE Trans. Signal Process. 59(7), 3099-3109 (2011)
Zhang, L, Boukas, EK, Baron, L, Karimi, HR: Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities. Int. J. Control 83(8), 1564-1572 (2010)
Yin, Y, Shi, P: Gain-scheduled robust fault detection on time-delay stochastic nonlinear systems. IEEE Trans. Ind. Electron. 58, 4908-4916 (2011)
Li, J, Park, JH, Ye, D: Fault detection filter design for switched systems with quantisation effects and packet dropout. IET Control Theory Appl. 11(2), 182-193 (2017)
Park, JH, Mathiyalagan, K, Sakthivel, R: Fault estimation for discrete-time switched nonlinear systems with discrete and distributed delays. Int. J. Robust Nonlinear Control 26(17), 3755-3771 (2016)
Ye, D, Park, JH, Fan, QY: Adaptive robust actuator fault compensation for linear systems using a novel fault estimation mechanism. Int. J. Robust Nonlinear Control 26(8), 1597-1614 (2016)
Li, J, Park, JH, Ye, D: Simultaneous fault detection and control design for switched systems with two quantized signals. ISA Trans. 66, 296-307 (2017)
He, S, Liu, F: Filtering-based robust fault detection of fuzzy jump systems. Fuzzy Sets Syst. 185, 95-110 (2011)
Wu, LG, Yao, XM, Zheng, WX: Generalized image fault detection for two-dimensional Markovian jump systems. Automatica 48, 1741-1750 (2012)
Li, P, Kadirkamanathan, V: Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems. IEEE Trans. Syst. Man Cybern., Part C, Appl. Rev. 31(3), 337-343 (2001)
Meskin, N, Khorasani, K: A geometric approach to fault detection and isolation of continuous-time Markovian jump linear systems. IEEE Trans. Autom. Control 55(6), 1343-1357 (2010)
Park, P, Ko, JW, Jeong, C: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235-238 (2011)
Boyd, S, Ghaoui, L, Feron, E, Balakrishnan, V: Linear Matrix Inequalities in Systems and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia (1994)
Gu, K: An integral inequality in the stability problem of time-delay systems. In: The 39th IEEE Conference on Decision Control, Sydney, Australia (2000)