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Observer design for delayed Markovian jump systems with output state saturation. (English) Zbl 1427.93269
Summary: This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.
93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
93B07 Observability
93D20 Asymptotic stability in control theory
Full Text: DOI
[1] Kong, S.-L.; Zhang, Z.-S., Optimal control of stochastic system with Markovian jumping and multiplicative noises, Acta Automatica Sinica, 38, 7, 1113-1118, (2012)
[2] Li, W.; Wu, Z., Output tracking of stochastic high-order nonlinear systems with Markovian switching, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 58, 6, 1585-1590, (2013) · Zbl 1369.93575
[3] Lakshmanan, S.; Rihan, F. A.; Rakkiyappan, R.; Park, J. H., Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters, Nonlinear Analysis: Hybrid Systems, 14, 1-15, (2014) · Zbl 1325.92062
[4] Xiong, J.; Lam, J.; Shu, Z.; Mao, X., Stability analysis of continuous-time switched systems with a random switching signal, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 59, 1, 180-186, (2014) · Zbl 1360.93756
[5] Duan, J.; Hu, M.; Yang, Y.; Guo, L., A delay-partitioning projection approach to stability analysis of stochastic Markovian jump neural networks with randomly occurred nonlinearities, Neurocomputing, 128, 459-465, (2014)
[6] Zheng, C.-D.; Zhang, Y.; Wang, Z., Stability analysis of stochastic reaction-diffusion neural networks with Markovian switching and time delays in the leakage terms, International Journal of Machine Learning and Cybernetics, 5, 1, 3-12, (2014)
[7] Kwon, N. K.; Park, B. Y.; Park, P., Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation, Optimal Control Applications and Methods, 37, 6, 1207-1216, (2016) · Zbl 1351.93165
[8] Park, B. Y.; Kwon, N. K.; Park, P., Stabilization of Markovian jump systems with incomplete knowledge of transition probabilities and input quantization, Journal of The Franklin Institute, 352, 10, 4354-4365, (2015) · Zbl 1395.93568
[9] Kao, Y.; Xie, J.; Wang, C., Stabilization of singular Markovian jump systems with generally uncertain transition rates, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 59, 9, 2604-2610, (2014) · Zbl 1360.93743
[10] Fan, H.; Liu, B.; Wang, W.; Wen, C., Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises, Automatica, 51, 200-209, (2015) · Zbl 1309.93133
[11] Shen, M.; Park, J. H.; Ye, D., A Separated Approach to Control of Markov Jump Nonlinear Systems with General Transition Probabilities, IEEE Transactions on Cybernetics, 46, 9, 2010-2018, (2016)
[12] Shi, P.; Yin, Y.; Liu, F.; Zhang, J., Robust control on saturated Markov jump systems with missing information, Information Sciences, 265, 123-138, (2014) · Zbl 1327.93400
[13] Qiu, L.; Shi, Y.; Yao, F. Q.; Xu, G.; Xu, B. G., Network-based robust control for linear system With two-channel random packet dropout and time delays, IEEE Transactions on Cybernetics, 45, 8, 1450-1462, (2015)
[14] Zhang, H.; Shi, Y.; Wang, J., Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays, International Journal of Control, 86, 10, 1824-1836, (2013) · Zbl 1312.93022
[15] Tian, E.; Yue, D.; Wei, G., Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities, Journal of The Franklin Institute, 350, 8, 2069-2083, (2013) · Zbl 1293.93699
[16] Li, H.; Shi, P.; Yao, D.; Wu, L., Observer-based adaptive sliding mode control for nonlinear Markovian jump systems, Automatica, 64, 133-142, (2016) · Zbl 1329.93126
[17] Zhong, X.; He, H.; Zhang, H.; Wang, Z., Optimal control for unknown discrete-time nonlinear markov jump systems using adaptive dynamic programming, IEEE Transactions on Neural Networks and Learning Systems, 25, 12, 2141-2155, (2014)
[18] Chang, R.; Fang, Y.; Liu, L.; Li, J., Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation, International Journal of Adaptive Control and Signal Processing, 31, 2, 255-274, (2017) · Zbl 1358.93005
[19] Liu, M.; Ho, D. W. C.; Shi, P., Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance, Automatica, 58, 5-14, (2015) · Zbl 1326.93020
[20] Shen, M. Q.; Ye, D.; Wang, Q. G., Event-triggered H8 filtering of Markov jump systems with general transition probabilities, Information Sciences, 418, 635-651, (2017)
[21] Shen, H.; Su, L.; Park, J. H., Reliable mixed H∞ passive control for T-S fuzzy delayed systems based on a semi-Markov jump model approach, Fuzzy Sets and Systems, 314, 79-98, (2017) · Zbl 1368.93156
[22] Li, F.; Wu, L.; Shi, P.; Lim, C.-C., State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties, Automatica, 51, 385-393, (2015) · Zbl 1309.93157
[23] Shi, P.; Zhang, Y.; Agarwal, R., Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps, Neurocomputing, 151, part 1, 168-174, (2014)
[24] Zhang, H.; Wang, J., State estimation of discrete-time Takagi-Sugeno fuzzy systems in a network environment, IEEE Transactions on Cybernetics, 45, 8, 1525-1536, (2014)
[25] Hu, J.; Chen, D.; Du, J., State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays, International Journal of General Systems, 43, 3-4, 387-401, (2014) · Zbl 1302.93201
[26] Wu, Z. G.; Shi, P.; Su, H.; Chu, J., Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data, IEEE Transactions on Cybernetics, 43, 6, 1796-1806, (2013)
[27] Wang, X.; Fang, J. A.; H, Y.; Dai, A. D., Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control, Nonlinear Dynamics, 79, 1, 47-61, (2015) · Zbl 1331.93076
[28] Allefeld, C.; Bialonski, S., Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 76, 6, (2007)
[29] Li, Z.-X.; Park, J. H.; Wu, Z.-G., Synchronization of complex networks with nonhomogeneous Markov jump topology, Nonlinear Dynamics, 74, 1-2, 65-75, (2013) · Zbl 1281.34088
[30] Shen, H.; Park, J. H.; Wu, Z.-G.; Zhang, Z., Finite-time H∞ synchronization for complex networks with semi-Markov jump topology, Communications in Nonlinear Science and Numerical Simulation, 24, 1-3, 40-51, (2015)
[31] Michael, H.; Chen, Z.; Wang, X.; Lam, J., Semi-global observer-based leader-following consensus with input saturation, IEEE Transactions on Industrial Electronics, 61, 6, 2842-2850, (2014)
[32] Zhang, Q.; Schaaf, C.; Seto, K. C., The Vegetation adjusted NTL Urban Index: A new approach to reduce saturation and increase variation in nighttime luminosity, Remote Sensing of Environment, 129, 32-41, (2013)
[33] Sun, W.; Gao, H.; Kaynak, O., Vibration isolation for active suspensions with performance constraints and actuator saturation, IEEE/ASME Transactions on Mechatronics, 20, 2, 675-683, (2015)
[34] Gao, S.; Dong, H.; Chen, Y.; Ning, B.; Chen, G.; Yang, X., Approximation-based robust adaptive automatic train control: an approach for actuator saturation, IEEE Transactions on Intelligent Transportation Systems, 14, 4, 1733-1742, (2013)
[35] Li, H. Y.; Hui, J. H.; Shi, P., Output-feedback based sliding mode control for fuzzy systems with actuator saturation, IEEE Transactions on Fuzzy Systems, 24, 6, 1282-1293, (2016)
[36] Sun, L.; Wang, Y.; Feng, G., Control design for a class of affine nonlinear descriptor systems with actuator saturation, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 60, 8, 2195-2200, (2015) · Zbl 1360.93302
[37] Klamkin, J.; Chang, Y.-C.; Ramaswamy, A.; Johansson, L. A.; Bowers, J. E.; DenBaars, S. P.; Coldren, L. A., Output saturation and linearity of waveguide unitraveling-carrier photodiodes, IEEE Journal of Quantum Electronics, 44, 4, 354-359, (2008)
[38] Klamkin, J.; Ramaswamy, A.; Johansson, L. A.; Chou, H.-F.; Sysak, M. N.; Raring, J. W.; Parthasarathy, N.; DenBaars, S. P.; Bowers, J. E.; Coldren, L. A., High output saturation and high-linearity uni-traveling-carrier waveguide photodiodes, IEEE Photonics Technology Letters, 19, 3, 149-151, (2007)
[39] Ji, X.; Sun, Y.; Su, H., Analysis and design for singular discrete linear systems subject to actuator saturation, Asian Journal of Control, 13, 2, 350-355, (2011) · Zbl 1222.93075
[40] Liu, H.; Boukas, E.-K.; Sun, F.; Ho, D. W. C., Controller design for Markov jumping systems subject to actuator saturation, Automatica, 42, 3, 459-465, (2006) · Zbl 1121.93027
[41] Ma, S.; Zhang, C., H∞ control for discrete-time singular Markov jump systems subject to actuator saturation, Journal of The Franklin Institute, 349, 3, 1011-1029, (2012) · Zbl 1273.93066
[42] Gonzaga, C. A. C.; Costa, O. L. V., Stochastic stabilization and induced 2-gain for discrete-time Markov jump Lur’e systems with control saturation, Automatica, 50, 9, 2397-2404, (2014) · Zbl 1297.93175
[43] Zhang, L.; Boukas, E.-K.; Haidar, A., Delay-range-dependent control synthesis for time-delay systems with actuator saturation, Automatica, 44, 10, 2691-2695, (2008) · Zbl 1155.93350
[44] Zhang, B. Y.; Xu, S. Y.; Zhang, Y. S.; Chu, Y. M., Delay-dependent stabilization for delayed Markovian jump systems subject to input saturation, Proceedings of the 29th Chinese Control Conference (CCC’10)
[45] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74, 14, 1447-1455, (2001) · Zbl 1023.93055
[46] Wang, G.; Xu, S.; Zou, Y., Stabilisation of hybrid stochastic systems by disordered controllers, IET Control Theory & Applications, 8, 13, 1154-1162, (2014)
[47] Wang, G.; Zhang, P.; Zhang, Q., A generalized robust H∞ filtering for singular Markovian jump systems and its applications, International Journal of Robust and Nonlinear Control, 24, 18, 3491-3507, (2014) · Zbl 1302.93219
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