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Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

Part of: Stochastic systems and control Equations and systems with randomness Stochastic analysis Special classes of linear operators

Published online by Cambridge University Press:  14 July 2016

Efraim Shmerling  and
Kenneth J. Hochberg
Efraim Shmerling*
Affiliation:
College of Judea and Samaria
Kenneth J. Hochberg*
Affiliation:
Bar-Ilan University
*
∗ Postal address: Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel.
∗∗ Postal address: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel. Email address: [email protected]
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Abstract

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

Keywords

Jump parameter systemsemi-Markov process

MSC classification

Primary: 60H25: Random operators and equations 47B80: Random operators 34F05: Equations and systems with randomness 93E03: Stochastic systems, general
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 442 - 454
Copyright
Copyright © Applied Probability Trust 2003 

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References

Borno, I. (1995). Parallel algorithms for optimal control of linear jump parameter systems and Markov processes. , Rutgers University.Google Scholar
Borno, I. (1995). Parallel computation of the solutions of coupled algebraic Lyapunov equations. Automatica J. IFAC 31, 1345–1347.CrossRefGoogle Scholar
Borno, I., and Gajic, A. (1995). Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. Comput. Math. Appl. 30, 1–4.CrossRefGoogle Scholar
Gajic, Z., and Qureshi, M. T. J. (1995). Lyapunov Matrix Equation in System Stability and Control. Academic Press, New York.Google Scholar
Mariton, M. (1990). Jump Linear Systems in Automatic Control. Marcel Dekker, New York.Google Scholar
Shmerling, E. (2000). Linear systems with random coefficients. , Bar-Ilan University.Google Scholar
Sworder, D. D., and Boyd, J. E. (1999). Estimation Problems in Hybrid Systems. Cambridge University Press.CrossRefGoogle Scholar