×

zbMATH — the first resource for mathematics

\(p\)-Moment stability of stochastic differential equations with impulsive jump and Markovian switching. (English) Zbl 1114.93092
Summary: This paper introduces some new concepts of \(p\)-moment stability for stochastic differential equations with impulsive jump and Markovian switching. Some stability criteria of \(p\)-moment stability for stochastic differential equations with impulsive jump and Markovian switching are obtained by using Lyapunov function method. An example is also discussed to illustrate the efficiency of the obtained results.

MSC:
93E03 Stochastic systems in control theory (general)
93C15 Control/observation systems governed by ordinary differential equations
93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Basak, G.K.; Bisi, A.; Ghosh, M.K., Stability of a random diffusion with linear drift, Journal of mathematics analysis and application, 202, 604-622, (1996) · Zbl 0856.93102
[2] Costa, O.L.V.; do Val, J.B.R.; Geromel, J.C., Continuous time state-feedback \(H_2\)-control of Markovian jump linear system via convex analysis, Automatica, 35, 259-268, (1999) · Zbl 0939.93041
[3] de Farias, D.P.; Geromel, J.C.; do Val, J.B.R.; Costa, O.L.V., Output feedback control of Markov jump linear systems in continuous-time, IEEE transactions on automatic control, 45, 5, 944-949, (2000) · Zbl 0972.93074
[4] do Val, J.B.R.; Geromel, J.C.; Goncalves, A.P.C., The \(H_2\)-control for jump linear systems: cluster observations of the Markov state, Automatica, 38, 343-349, (2002) · Zbl 0991.93125
[5] Ji, Y.; Chizeck, H.J., Controllability, stability and continuous-time Markovian jump linear quadratic control, IEEE transactions on automatic control, 35, 777-788, (1990) · Zbl 0714.93060
[6] Liu, X., Impulsive stabilization and applications to population growth models, Rocky mountain journal of mathematics, 25, 269-284, (1995)
[7] Liu, X.; Rohlf, K., Impulsive control of Lotka-Volterra models, Mathematical control information, 15, 381-395, (1998)
[8] Mao, X., Stability of stochastic differential equations with Markovian switching, Stochastic process and application, 79, 1, 45-67, (1999) · Zbl 0962.60043
[9] Mariton, M., Jump linear systems in automatic control, (1990), Marcel Dekker New York
[10] Oksendal, B., Stochastic differential equations, (1995), Springer New York
[11] Skorohod, A.V., Asymptotic methods in the theory of stochastic differential equations, (2004), American Mathematical Society Providence, RI
[12] Sun, J.T.; Zhang, Y.P., Stability analysis of impulsive control systems, IEE Proceedings of control theory and applications, 150, 4, 331-334, (2003)
[13] Sun, J.T.; Zhang, Y.P.; Wu, Q.D., Less conservative condition for asymptotic stability of impulsive control systems, IEEE transactions on automatic control, 48, 5, 829-831, (2003) · Zbl 1364.93691
[14] Wu, S.J.; Han, D.; Meng, X.Z., p-moment stability of stochastic differential equations with jumps, Applied mathematics and computation, 152, 2, 505-519, (2004) · Zbl 1042.60036
[15] Xu, S.; Chen, T.; Lam, J., Robust \(H_\infty\) filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE transactions on automatic control, 48, 5, 900-907, (2003) · Zbl 1364.93816
[16] Yang, T., Impulsive control, IEEE transactions on automatic control, 44, 1081-1083, (1999) · Zbl 0954.49022
[17] Yang, T., Impulsive systems and control: theory and applications, (2001), Nova Science Publishers Huntington, NY
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.