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

Yueyuan Zhang; Yanyan Yin; Fei Liu

doi:10.3934/jimo.2020105

Article Contents

2021, Volume 17, Issue 6: 3013-3026. Doi: 10.3934/jimo.2020105

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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
^* Corresponding author: Yueyuan Zhang

Received: August 2019

Revised: December 2019

Early access: June 2020

Published: November 2021

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

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. The response of the jump mode

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Figure 2. The response of the system state

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Figure 3. The estimation of the domain attraction for different modes

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Table 1. 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

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