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

Research output: Contribution to journalArticlepeer-review

23 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 languageEnglish
Pages (from-to)191-205
Number of pages15
JournalApplied Mathematics and Computation
Volume342
DOIs
Publication statusPublished - 2019 Feb 1

Bibliographical 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:
© 2018 Elsevier Inc.

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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