$ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method

Xingyue Liang; Jianwei Xia; Guoliang Chen; Huasheng Zhang; Zhen Wang

doi:10.3934/dcdss.2020368

Article Contents

2021, Volume 14, Issue 4: 1329-1343. Doi: 10.3934/dcdss.2020368

This issue Previous Article Event-based fault detection for interval type-2 fuzzy systems with measurement outliers Next Article Pullback exponential attractors for differential equations with delay

$ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method

1.
Liaocheng University, School of Mathematics Science, Liaocheng 252000, P. R. China
2.
Shandong University of Science and Technology, College of Mathematics and Systems Science, Qingdao 266590, China

^* Corresponding author: Jianwei Xia
^* Corresponding author: Jianwei Xia

Received: July 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: April 2021

The first author is supported by the National Natural Science Foundation of China under Grants 61573177, 61773191, 61973148

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Abstract

This paper investigates the problems of $ \mathcal{H}_{\infty} $ performance analysis and sampled-data control about fuzzy Markovian jump systems. Firstly, in order to make full use of the information of both intervals $ x(t_{k}) $ to $ x(t) $ and $ x(t) $ to $ x(t_{k+1}) $, we construct the mode-dependent Lyapunov function, which consists of a two-sided closed-loop function. Built on the above Lyapunov function, the stochastically stable conditions with less conservative are given by using linear matrices inequalities (LMIs). Then, a state feedback controller is presented for the studied systems. At last, an example is offered to illustrate the efficiency of our main results.

Keywords:

fuzzy Markovian jump systems,
$ \mathcal{H}_{\infty} $ performance analysis,
sampled-data control,
fuzzy control,
two-sided looped function.

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

Citation:

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Table 1. $ \gamma_{max} $ for $ h_{min} = 0 $ and different $ h_{max} $

	$ h_{max} $	0.05	0.15	0.25	0.35
	$ \gamma $	$ 1.7320 $	1.7678	1.8246	1.9285

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Table 2. $ \gamma_{max} $ for $ h_{max} = h_{min} $

	$ h $	0.05	0.15	0.25	0.35
	$ \gamma $	$ 1.7299 $	1.7576	1.7982	1.8659

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