Abstract
It is known that Markov jump systems have finite modes which may jump from one to another at different times and between different modes. A system with “jumping” character may be modeled as a hybrid system, and the parameter jumps among different modes can be seen as discrete events [119]. Until now, only a little results on Markov jump DOSs have been obtained. Stability analysis of Markov jump DOSs over networks has been given in [167]. By letting each intermittent interval satisfy the corresponding Markov jump process, a class of DOSs has been used to describe NCSs in [169]. A problem on robust stabilization has been concerned of singular Markov jump systems with time-varying delays and parameter uncertainties [208]. There are also several results along a line of actuator saturation for the Markov jump systems.
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References
H. Liu, F. Sun, E.-K. Boukas, D. Ho, Controller design for Markov jumping systems subject to actuator saturation. Automatica 42(3), 459–465 (2006)
H. Liu, F. Sun, E. Boukas, Robust control of uncertain discrete-time Markovian jump systems with actuator saturation. Int. J. Control 79(7), 805–812 (2006)
S. Ma, C. Zhang, S. Zhu, Robust stability for discrete-time uncertain singular Markov jump systems with actuator saturation. IET Control Theory Appl. 5(2), 255–262 (2011)
P. Shi, Y. Xia, G.-P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006)
Y. Wang, C. Wang, Z. Zuo, Controller synthesis for Markovian jump systems with incomplete knowledge of transition probabilities and actuator saturation. J. Frankl. Inst. 348(9), 2417–2429 (2011)
H. Yang, Y. Xia, P. Shi, M. Fu, Stability analysis for high frequency networked control systems. IEEE Trans. Autom. Control 57(10), 2694–2700 (2012)
H. Yang, Y. Xia, P. Shi, B. Liu, Guaranteed cost control of networked control systems based on delta operator Kalman filter. Int. J. Adapt. Control Signal Process. 27(8), 701–717 (2013)
H. Yang, Y. Xia, P. Shi, L. Zhao, Analysis and Synthesis of Delta Operator Systems (Springer, Berlin/Heidelberg, 2012)
G. Zhuang, J. Xia, B. Zhang, W. Sun, Robust normalisation and PCD state feedback control for uncertain singular Markovian jump systems with time-varying delays. IET Control Theory Appl. 12(3), 419–427 (2018)
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Yang, H., Xia, Y., Geng, Q. (2019). Robust Control for Markov Jump Systems. In: Analysis and Synthesis of Delta Operator Systems with Actuator Saturation. Studies in Systems, Decision and Control, vol 193. Springer, Singapore. https://doi.org/10.1007/978-981-13-3660-7_16
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DOI: https://doi.org/10.1007/978-981-13-3660-7_16
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