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.
| Language | English |
|---|---|
| Pages | 191-205 |
| Number of pages | 15 |
| Journal | Applied Mathematics and Computation |
| Volume | 342 |
| DOIs | |
| Publication status | Published - 2019 Feb 1 |
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Keywords
- Reciprocally convex inequality
- Semi-Markovian jump system
- Stochastic stability
- Time-varying delay
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
Cite this
A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay. / Zhang, Dian; Cheng, Jun; Ahn, Choon Ki; Ni, Hongjie.
In: Applied Mathematics and Computation, Vol. 342, 01.02.2019, p. 191-205.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay
AU - Zhang, Dian
AU - Cheng, Jun
AU - Ahn, Choon Ki
AU - Ni, Hongjie
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
UR - http://www.scopus.com/inward/record.url?scp=85054314608&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054314608&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2018.09.035
DO - 10.1016/j.amc.2018.09.035
M3 - Article
VL - 342
SP - 191
EP - 205
JO - Applied Mathematics and Computation
T2 - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -