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Volume 6 Issue 6
Nov.  2019

IEEE/CAA Journal of Automatica Sinica

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Yan Zhang, Ke Lou and Yuan Ge, "New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1499-1505, Nov. 2019. doi: 10.1109/JAS.2016.7510229
 Citation: Yan Zhang, Ke Lou and Yuan Ge, "New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1499-1505, Nov. 2019.

# New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

##### doi: 10.1109/JAS.2016.7510229
Funds:

the National Natural Science Foundation of China 61403001

the National Natural Science Foundation of China 61572032

the Natural Science Foundation of Anhui Province of China 1508085QF136

part by the Natural Science Foundation of Universities of Anhui Province of China KJ2016A058

• This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems (MJTDSs), whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance, auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function (ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally, numerical examples are given to show the effectiveness and the merits of the proposed method.

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## Highlights

• Inspired by auxiliary function-based double integral inequality, an augmented Lyapunov-Krasovskii function (ALKF) including augmented term and triple integral term is constructed in this paper to investigate the stability of MJTDSs.
• Compared with Pi satisfying the condition Pi > 0, the constraint condition to guarantee the positiveness of ALKF is weakened by using auxiliary function-based double integral inequality, extended Wirtinger’s inequality and Jensen inequality to estimate the lower bound of the ALKF.
• The above three inequalities are used to estimate the upper bound of weak infinitesimal generator of the ALKF, as a result, the more accurate approximation bounds with a fewer variables are derived.
• Consequently, the new criterion on delay-dependent stability for MJTDSs is obtained in this paper. Compared with previous criteria, our results require fewer scalar variables and have less conservative.

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