A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay

Dian Zhang; Jun Cheng; Choon Ki Ahn; Hongjie Ni

doi:10.1016/j.amc.2018.09.035

A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay

Dian Zhang, Jun Cheng, Choon Ki Ahn, Hongjie Ni

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ₁ ≤ τ(t) ≤ τ₂. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ₁(t) ≤ τ(t) ≤ τ₂(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

Original language	English
Pages (from-to)	191-205
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	342
DOIs	https://doi.org/10.1016/j.amc.2018.09.035
Publication status	Published - 2019 Feb 1

Keywords

Reciprocally convex inequality
Semi-Markovian jump system
Stochastic stability
Time-varying delay

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2018.09.035

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title = "A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay",

abstract = "This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.",

keywords = "Reciprocally convex inequality, Semi-Markovian jump system, Stochastic stability, Time-varying delay",

author = "Dian Zhang and Jun Cheng and {Ki Ahn}, Choon and Hongjie Ni",

note = "Funding Information: This work was supported by the National Natural Science Foundation of China ( 61703150 , 11701163 ), the Natural Science Foundation of Shandong Provinces of China ( ZR2018LC010 ), the Program for Innovative Research Team of the Higher Education Institutions of Hubei Province ( T201812 ). Funding Information: This work was supported by the National Natural Science Foundation of China (61703150, 11701163), the Natural Science Foundation of Shandong Provinces of China (ZR2018LC010), the Program for Innovative Research Team of the Higher Education Institutions of Hubei Province (T201812). Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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doi = "10.1016/j.amc.2018.09.035",

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AU - Zhang, Dian

AU - Cheng, Jun

AU - Ki Ahn, Choon

AU - Ni, Hongjie

N1 - Funding Information: This work was supported by the National Natural Science Foundation of China ( 61703150 , 11701163 ), the Natural Science Foundation of Shandong Provinces of China ( ZR2018LC010 ), the Program for Innovative Research Team of the Higher Education Institutions of Hubei Province ( T201812 ). Funding Information: This work was supported by the National Natural Science Foundation of China (61703150, 11701163), the Natural Science Foundation of Shandong Provinces of China (ZR2018LC010), the Program for Innovative Research Team of the Higher Education Institutions of Hubei Province (T201812). Publisher Copyright: © 2018 Elsevier Inc.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

AB - This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

KW - Reciprocally convex inequality

KW - Semi-Markovian jump system

KW - Stochastic stability

KW - Time-varying delay

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DO - 10.1016/j.amc.2018.09.035

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VL - 342

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EP - 205

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -

A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay

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Keywords

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