Stability and output feedback control for singular Markovian jump delayed systems

Jian Chen; Tao Zhang; Ziye Zhang; Chong Lin; Bing Chen

doi:10.3934/mcrf.2018019

Article Contents

2018, Volume 8, Issue 2: 475-490. Doi: 10.3934/mcrf.2018019

This issue Previous Article A second-order stochastic maximum principle for generalized mean-field singular control problem Next Article

Stability and output feedback control for singular Markovian jump delayed systems

1.
College of Automation Engineering, Qingdao University of Technology, Qingdao 266555, China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
3.
Institute of Complexity Science, Qingdao University, Qingdao 266073, China

* Corresponding author: Jian Chen
* Corresponding author: Jian Chen

Received: August 31, 2017

Revised: December 31, 2017

Published: May 2018

The first author is supported by NSF grants 61673227 and 61503222.

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Abstract

This paper is concerned with the admissibility analysis and control synthesis for a class of singular systems with Markovian jumps and time-varying delay. The basic idea is the use of an augmented Lyapunov-Krasovskii functional together with a series of appropriate integral inequalities. Sufficient conditions are established to ensure the systems to be admissible. Moreover, control design via static output feedback (SOF) is derived to achieve the stabilization for singular systems. A new algorithm is built to solve the SOF controllers. Examples are given to show the effectiveness of the proposed method.

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

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Figure 1. The closed-loop response curves in Example 1

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Figure 2. Jumping modes

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Table 1. Maximun allowable upper bounds of time delay $\tau$ for Example 1

$ \pi_{11} $	-0.4	-0.55	-0.7	-0.85	-1.00
[26]	0.6078	0.5894	0.5768	0.5675	0.5603
[23]	0.6322	0.6120	0.5981	0.5881	0.5805
[18]	0.8181	0.7815	0.7597	0.7473	0.7377
Corollary 1	0.9874	0.9312	0.8944	0.8684	0.8491

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