April  2016, 12(2): 471-486. doi: 10.3934/jimo.2016.12.471

$p$th Moment absolute exponential stability of stochastic control system with Markovian switching

1. 

Department of Mathematics, College of Science, China University of Petroleum, Beijing 102249, China, China, China, China

Received  September 2014 Revised  February 2015 Published  June 2015

In this paper we discuss the $p$th moment absolute exponential stability of stochastic control system with Markovian switching. We first give a new concept of $p$th moment absolute exponential stability, then we establish some theorems under different hypotheses to guarantee the system $p$th moment absolutely exponentially stable. These sufficient conditions in our theorems are algebraic criteria in terms of matrix inequalities, and we introduce an $M$-method with MATLAB to compute them. Finally, some examples are given to illustrate our results.
Citation: Yi Zhang, Yuyun Zhao, Tao Xu, Xin Liu. $p$th Moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial & Management Optimization, 2016, 12 (2) : 471-486. doi: 10.3934/jimo.2016.12.471
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Automation and Remote Control, 67 (2006), 1811-1846. doi: 10.1134/S0005117906110051.  Google Scholar

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Automation and Remote Control, 22 (1962), 857-875.  Google Scholar

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show all references

References:
[1]

Journal of Mathematical Analysis and Applications, 202 (1996), 604-622. doi: 10.1006/jmaa.1996.0336.  Google Scholar

[2]

Siberian Mathematical Journal, 28 (1987), 381-393.  Google Scholar

[3]

Journal of Industrial and Management Optimization, 8 (2012), 591-609. doi: 10.3934/jimo.2012.8.591.  Google Scholar

[4]

Proceedings of the National Academy of Sciences of the United States of America, 49 (1963), 201. doi: 10.1073/pnas.49.2.201.  Google Scholar

[5]

Ukrainian Mathematical Journal, 40 (1988), 616-621. doi: 10.1007/BF01057179.  Google Scholar

[6]

Academic Press, New York, 1967.  Google Scholar

[7]

Elsevier, 2007. doi: 10.1016/S1574-6917(07)05001-5.  Google Scholar

[8]

2nd edition, Springer, 2008. doi: 10.1007/978-1-4020-8482-9.  Google Scholar

[9]

Springer, 2003. doi: 10.1007/978-1-4612-0017-8.  Google Scholar

[10]

Automation and Remote Control, 67 (2006), 1610-1644. doi: 10.1134/S0005117906100043.  Google Scholar

[11]

Applied Mathematics and Mechanics, 8 (1944), 246-248. Google Scholar

[12]

Automatic Control, IEEE Transactions on, 18 (1973), 266-270.  Google Scholar

[13]

Journal of Industrial and Management Optimization, 11 (2015), 329-343. doi: 10.3934/jimo.2015.11.329.  Google Scholar

[14]

Stochastic Processes and Their Applications, 79 (1999), 45-67. doi: 10.1016/S0304-4149(98)00070-2.  Google Scholar

[15]

WSEAS Trans. Circuits, 1 (2002), 68-73.  Google Scholar

[16]

Imperial College Press, 2006. doi: 10.1142/p473.  Google Scholar

[17]

Elsevier, 2007. doi: 10.1533/9780857099402.  Google Scholar

[18]

Automation and Remote Control, 67 (2006), 1811-1846. doi: 10.1134/S0005117906110051.  Google Scholar

[19]

Automation and Remote Control, 22 (1962), 857-875.  Google Scholar

[20]

Springer, 2011. doi: 10.1007/978-0-85729-256-8.  Google Scholar

[21]

Springer, 2000. doi: 10.1007/BFb0109998.  Google Scholar

[22]

Science Press, Beijing, 1986. Google Scholar

[23]

Automatic Control, IEEE Transactions on, 55 (2010), 2429-2433. doi: 10.1109/TAC.2010.2060173.  Google Scholar

[24]

Discrete and Continuous Dynamical Systems-Series B, 16 (2011), 1185-1195. doi: 10.3934/dcdsb.2011.16.1185.  Google Scholar

[25]

Abstract and Applied Analysis, 2014 (2014), Hindawi Publishing Corporation. doi: 10.1155/2014/126836.  Google Scholar

[26]

Soviet Math. Dokl, 3 (1962), 620-623. Google Scholar

[27]

Nonlinear Analysis: Hybrid Systems, 14 (2014), 86-98. doi: 10.1016/j.nahs.2014.05.004.  Google Scholar

[28]

In Abstract and Applied Analysis, 2013 (2013), Hindawi Publishing Corporation.  Google Scholar

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