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

7 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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Zhang, D., Cheng, J., Ahn, C. K., & Ni, H. (2019). A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay. Applied Mathematics and Computation, 342, 191-205. https://doi.org/10.1016/j.amc.2018.09.035

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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.",

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AU - Zhang, Dian

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AU - Ahn, Choon Ki

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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.

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