# American Institute of Mathematical Sciences

November  2021, 17(6): 3013-3026. doi: 10.3934/jimo.2020105

## Robust observer-based control for discrete-time semi-Markov jump systems with actuator saturation

 1 School of Mechanical and Electric Engineering, Soochow University, Suzhou 215131, China 2 Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA 6845, Australia, Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation,Jiangnan University, Wuxi 214122, China

* Corresponding author: Yueyuan Zhang

Received  August 2019 Revised  December 2019 Published  November 2021 Early access  June 2020

Fund Project: This work was partially supported by The National Natural Science Foundation of China (61773183)

This paper investigates the control synthesis for discrete-time semi-Markov jump systems with nonlinear input. Observer-based controllers are designed in this paper to achieve a better performance and robustness. The nonlinear input caused by actuator saturation is considered as a group of linear controllers in the convex hull. Moreover, the elapse time and mode dependent Lyapunov functions are investigated and sufficient conditions are derived to guarantee the $H_\infty$ performance index. The largest domain of attraction is estimated as the existing saturation in the system. Finally, a numerical example is utilized to verify the effectiveness and feasibility of the developed strategy.

Citation: Yueyuan Zhang, Yanyan Yin, Fei Liu. Robust observer-based control for discrete-time semi-Markov jump systems with actuator saturation. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3013-3026. doi: 10.3934/jimo.2020105
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##### References:
The response of the jump mode
The response of the system state
The estimation of the domain attraction for different modes
The error $\sigma$ for different maximum sojourn time in different mode
 Maximum sojourn time $T^i_{max}$ error $\sigma$ $T^1_{max}$ $T^2_{max}$ $T^3_{max}$ $\sigma$ 3 4 3 ln(0.032)=-3.442 4 4 3 ln(0.1048)=-2.2557 4 4 4 ln(0.1061)=-2.2434 6 6 6 ln(0.4859)=-0.7218 8 8 8 ln(0.9028)=-0.1023 10 10 10 ln(1)=0
 Maximum sojourn time $T^i_{max}$ error $\sigma$ $T^1_{max}$ $T^2_{max}$ $T^3_{max}$ $\sigma$ 3 4 3 ln(0.032)=-3.442 4 4 3 ln(0.1048)=-2.2557 4 4 4 ln(0.1061)=-2.2434 6 6 6 ln(0.4859)=-0.7218 8 8 8 ln(0.9028)=-0.1023 10 10 10 ln(1)=0
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