Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control

Hui Lv; Xing'an Wang

doi:10.3934/naco.2020020

Article Contents

2021, Volume 11, Issue 1: 127-142. Doi: 10.3934/naco.2020020

This issue Previous Article A PID control method based on optimal control strategy Next Article

Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control

Hui Lv^1, , and
Xing'an Wang^2, ,

1.
Key Laboratory of Advanced Design, and, Intelligent Computing, Ministry of Education, School of Software, Dalian University, Dalian, 116622, China
2.
College of Environmental and Chemical Engineering, Dalian University, Dalian, 116622, China

^* Corresponding author: lh8481@tom.com; wangxingan@dlu.edu.cn
^* Corresponding author: lh8481@tom.com; wangxingan@dlu.edu.cn

Received: May 2019

Revised: October 2019

Early access: March 2020

Published: March 2021

The first author is supported by National Natural Science Foundation of China (No.61802040), Natural Science Foundation of Liaoning Province (No.20180551241) and High-level Talent Innovation Support Program of Dalian City (No.2018RQ75). The second author is supported by National Key Laboratory for Precision Hot Processing of Metals(No.614290903061808) and Doctoral Starting Foundation of Dalian University (No.2017QL024)

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Abstract

This paper investigates the problem of dissipative control for a class of uncertain singular Markovian jump systems. Different from the traditional control strategy, a derivative gain and impulsive control part are added in the proposed controller. A linearization approach via congruence transformations is proposed to solve the feedback design problem. In addition, the derived results contain $ H_{\infty} $ and passive control as special cases. Finally, examples are provided to illustrate the effectiveness and applicability of the proposed methods.

Keywords:

Dissipative control,
Uncertain singular Markovian jump systems,
Impulsive control.

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

Citation:

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Figure 1. The Markov process

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Figure 2. The state trajectories of the open-loop system (when $ \omega(t) = 0 $)

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Figure 3. The state trajectories of the closed-loop system (when $ \omega(t) = 0 $)

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Table 1. Minimum attenuation level calculated by different methods

$ \gamma_{min} $	$ \rho=-0.5 $	$ \rho=0 $	$ \rho=0.5 $	$ \rho=1 $	$ \rho=1.5 $
Theorem 10 ([28])	1.2704	1.5821	2.2548	4.4628	————
Corollary 3.4 ($ K_{ei}=0 $)	1.1724	1.1738	1.1743	1.1749	1.1753
Corollary 3.4 ($ K_{ei}\neq0 $)	1.1040	1.1050	1.1059	1.1067	1.1074

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