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Some peculiarities of the general method of Lyapunov functionals construction. (English) Zbl 1015.39001
Authors’ abstract: The general method of Lyapunov functionals construction for stability investigation of stochastic hereditary systems which was proposed and developed before is considered. Some features of this method for difference systems which allow one to use the method more effectively are discussed.
Reviewer: Fozi Dannan (Doha)

MSC:
39A11 Stability of difference equations (MSC2000)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D30 Lyapunov and storage functions
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[1] Kolmanovskii, V.B.; Shaikhet, L.E., General method of Lyapunov functionals construction for stability investigations of stochastic difference equations, (), 397-439 · Zbl 0846.93083
[2] Kolmanovskii, V.B.; Shaikhet, L.E., Stability of stochastic hereditary systems, Avtomatika i telemekhanika, 7, 66-85, (1993)
[3] Kolmanovskii, V.B.; Shaikhet, L.E., On one method of Lyapunov functional construction for stochastic hereditary systems, Differentialniye uravneniya, 11, 1909-1920, (1993) · Zbl 0815.34068
[4] Kolmanovskii, V.B.; Shaikhet, L.E., New results in stability theory for stochastic functional differential equations (SFDEs) and their applications, (), 167-171 · Zbl 0811.34062
[5] Shaikhet, L.E., Stability in probability of nonlinear stochastic systems with delay, Matematicheskiye zametki, 57, 1, 142-146, (1995) · Zbl 0843.93086
[6] Shaikhet, L.E., Stability in probability of nonlinear stochastic hereditary systems, Dynamic systems and applications, 4, 2, 199-204, (1995) · Zbl 0831.60075
[7] Kolmanovskii, V.B.; Rodionov, A.M., On the stability of some discrete Volterra processes, Avtomatika i telemekhanika, 2, 3-13, (1995)
[8] Kolmanovskii, V.B.; Shaikhet, L.E., A method of Lyapunov functional construction for stochastic differential equations of neutral type, Differentialniye uravneniya, 11, 1851-1857, (1995)
[9] Shaikhet, L.E., Modern state and development perspectives of Lyapunov functionals method in the stability theory of stochastic hereditary systems, Theory of stochastic processes, 2, 18, No. 1/2, 248-259, (1996) · Zbl 0893.60029
[10] Shaikhet, L.E., Stability of stochastic hereditary systems with Markov switching, Theory of stochastic processes, 2, 18, No. 3/4, 180-185, (1996) · Zbl 0939.60049
[11] Kolmanovskii, V.B.; Shaikhet, L.E., Asymptotic behaviour of some systems with discrete time, Avtomatika i telemekhanika, 12, 58-66, (1996)
[12] Shaikhet, L.E.; Shaikhet, L.E., Some problems of stability for stochastic difference equations, 15^{th} world congress on scientific computation, modelling and applied mathematics, Computational mathematics, 1, 257-262, (1997), IMACS97, Berlin · Zbl 0987.93076
[13] Shaikhet, L.E., Problems of the stability for stochastic difference equations, Theory of stochastic processes (Proceedings of the 2^{nd} scandinavian-Ukrainian conference, June 8-13, 1997 umea, Sweden), 3, 19, No. 3/4, 403-411, (1997) · Zbl 0930.39014
[14] Shaikhet, L.E., Necessary and sufficient conditions of asymptotic Mean square stability for stochastic linear difference equations, Appl. math. lett., 10, 3, 111-115, (1997) · Zbl 0883.39005
[15] Kolmanovskii, V.B.; Shaikhet, L.E., About stability of some stochastic Volterra equations, Differentialniye uravneniya, 11, 1495-1502, (1997)
[16] Ford, N.J.; Edwards, J.T.; Roberts, J.A.; Shaikhet, L.E., Stability of a difference analogue for a nonlinear integro differential equation of convolution type, Numerical analysis report, (1997), University of Manchester, No. 312
[17] Kolmanovskii, V.B.; Shaikhet, L.E., Matrix Riccati equations and stability of stochastic linear systems with nonincreasing delays, Functional differential equations, 4, 3/4, 279-293, (1997) · Zbl 1148.93346
[18] Beretta, E.; Kolmanovskii, V.; Shaikhet, L., Stability of epidemic model with time delays influenced by stochastic perturbations, Mathematics and computers in simulation (special issue “delay systems”), 45, 3/4, 269-277, (1998) · Zbl 1017.92504
[19] Kolmanovskii, V.B.; Shaikhet, L.E., Riccati equations in stability of stochastic linear systems with delay, Avtomatika i telemekhanika, 10, 35-54, (1998) · Zbl 1123.34323
[20] Kolmanovskii, V.B.; Shaikhet, L.E., Riccati equations and stability of stochastic linear systems with distributed delay, (), 97-100
[21] Shaikhet, G.; Shaikhet, L., Stability of stochastic linear difference equations with varying delay, (), 101-104
[22] Shaikhet, L.E., Stability of predator-prey model with aftereffect by stochastic perturbations, Stability and control: theory and application, 1, 1, 3-13, (1998)
[23] Paternoster, B.; Shaikhet, L., Stability in probability of nonlinear stochastic difference equations, Stability and control: theory and application, 2, 1-2, 25-39, (1999)
[24] Paternoster, B.; Shaikhet, L., About stability of nonlinear stochastic difference equations, Appl. math. lett., 13, 5, 27-32, (2000) · Zbl 0959.60056
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