Interests
Stability theory for stochastic functional-differential and difference equations, Method of Lyapunov functionals construction, Optimal control of hereditary systems.
Books
- Shaikhet L. Optimal control of stochastic difference Volterra equations. Springer, 2015. link.
- Shaikhet L. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Dordrecht, Heidelberg, New York, London, 2013. 342 p. link.
- Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer, London, Dordrecht, Heidelberg, New York, 2011. 370 p. link.
- Control of systems with aftereffect. (with Kolmanovskii V.B.). Translations of mathematical monographs, vol.157. American Mathematical Society, Providence, RI, 1996. 336 p. link
- Control of hereditary systems. (with Andreyeva E.A. and Kolmanovskii V.B.). Moscow, Nauka. 1992. 336 p. (in Russian). download (DJVU)
Recent Publications
2017
- (Shaikhet L.) Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations. International Journal of Robust and Nonlinear Control, 2017, V.27, 915?924. Published online 24 July 2016 in Wiley Online Library. download
- (Fridman E., Shaikhet L.) Stabilization by using artificial delays: an LMI approach. Automatica, 81 (2017), 429-437. download
- (Shaikhet L.) About some asymptotic properties of solution of stochastic delay differential equation with a logarithmic nonlinearity. Functional Differential Equations, 2017, V.24, N.1-2, 57-67. download
- (Chatzarakis G., Shaikhet L.) Oscillation criteria for difference equations of non-monotone arguments. Advances in Difference Equations 2017, 2017:62 (27 February 2017), 16 pages. download
- (Shaikhet L.) Stability of equilibriums of stochastically perturbed delay differential neoclassical growth model. Discrete and Continuous Dynamical Systems. Series B. 2017. V.22, N.4, p.1565-1573. download
2016
- (Shaikhet L., Korobeinikov A.) Stability of a stochastic model for HIV-1 dynamics within a host. Applicable Analysis: An International Journal, 2016, V.95, N.6, p.1228-1238. Published online: 22 Jun 2015 download
- (Fridman E., Shaikhet L.) Delay-induced stability of vector second-order systems via simple Lyapunov functionals. Automatica 74(2016) 288-296. doi: 10.1016/j.automatica.2016. 07.034 download
2015
- (Shaikhet L. ) Stability of equilibrium states for a stochastically perturbed exponential type system of difference equations. Journal of Computational and Applied Mathematics. 2015. V.290, p.92-103 download
2014
- (Shaikhet L. ) Stability of equilibrium states for a stochastically perturbed Mosquito population equation. Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and Algorithms. 2014. V.21, N.2, p.185-196 download
- (Shaikhet L. ) Stability of a positive equilibrium state for a stochastically perturbed mathematical model of glassy-winged sharpshooter population. Mathematical biosciences and engineering. 2014. V.11, N.5, p.1167-1174. doi:10.3934/mbe.2014.11.1167 download
- (Shaikhet L., Korobeinikov A. ) Stability of a stochastic model for HIV-1 dynamics within a host. CRM (Centre de Recerca Matematica) Preprint Series number 1191, May 2014, 13p. download
- (Caraballo T., Shaikhet L. ) Stability of delay evolution equations with stochastic perturbations. Communications on Pure and Applied Analysis. September 2014. V.13, N.5, p.2095-2113. doi:10.3934/cpaa.2014.13.2095 download
- (Santonja F-J., Shaikhet L. ) Probabilistic stability analysis of social obesity epidemic by a delayed stochastic model. Nonlinear Analysis: Real World Applications. 2014, V.17, p. 114-125. download
2012
- (Santonja F-J., Shaikhet L. ) Analysing social epidemics by delayed stochastic models. Discrete Dynamics in Nature and Society, vol. 2012, Article ID 530472, 13 pages, 2012. doi:10.1155/2012/530472. download
- (Shaikhet L.) Two unsolved problems in the stability theory of stochastic differential equations with delay. Applied Mathematics Letters. 2012, V.25, N.3, p.636-637. download
- (Shaikhet L.) Stability of equilibrium points of differential equation with fractional nonlinearity and stochastic perturbations. Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications & Algorithms. V.19, N.6, 2012, p.709-729. download
2011
- (Shaikhet L.) About an unsolved stability problem for a stochastic difference equation with continuous time. Journal of Difference Equations and Applications. 2011, V.17, N.3, p.441-444. download
- (Shaikhet L., Roberts J. ) Asymptotic stability analysis of a stochastic Volterra integro-differential equation with fading memory. Dynamics of Continuous, Discrete and Impulsive Systems; Series B: Applications & Algorithms. 2011, V.18, p.749-770. download
2010
- (Shaikhet L.) Some new aspects of Lyapunov-type theorems for stochastic differential equations of neutral type. SIAM J. Control and Optimization. 2010, Vol. 48, No. 7, p. 4481-4499. download
2009
- (Shaikhet L.) Improved condition for stabilization of controlled inverted pendulum under stochastic perturbations. Discrete and Continuous Dynamical Systems. 2009, V.24, N. 4, p. 1335-1343. download
2008
- (Shaikhet L.) Stability of a positive point of equilibrium of one nonlinear system with aftereffect and stochastic perturbations. Dynamic Systems and Applications. 2008, Vol.17, p.235-253. download
- (Rodkina A., Schurz H., Shaikhet L.) Almost sure stability of some stochastic dynamical systems with memory. Discrete and Continuous Dynamical Systems, 2008. Vol.21, N.2, June 2008, p.571-593. download
- (Paternoster B., Shaikhet L.) Stability of equilibrium points of fractional difference equations with stochastic perturbations. Advances in Difference Equations. 2008. V.2008, Article ID 718408, 21 pages. download
2007
- (Paternoster B., Shaikhet L.) Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity. Advances in Difference Equations. 2007. V.2007, Article ID 65012, 13 pages. download
- (Caraballo T., Real J., Shaikhet L.) Method of Lyapunov functionals construction in stability of delay evolution equations.Journal of Mathematical Analysis and Applications. 2007. V.334, N.2, p.1130-1145. download
- (Bradul N., Shaikhet L.) Stability of the positive point of equilibrium of Nicholson's blowflies equation with stochastic perturbations: numerical analysis. Discrete Dynamics in Nature and Society, 2007, V.2007, Article ID 92959, 25 pages. download
- (Luo J., Shaikhet L.) Stability in Probability of Nonlinear Stochastic Volterra Difference Equations with Continuous Variable. Stochastic Analysis and Applications, 2007, Vol.25, No.6, p.1151-1165. download
2006
- (Shaikhet L., Roberts J.) Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations. Advances in Difference Equations. 2006. V.2006, Article ID 73897, 22 pages. download
- (Shaikhet L.) Some new aspect of Lyapunov type theorems for stochastic difference equations with continuous time. Asian Journal of Control. 2006. Vol.8, N.1, p.76-81. download
- (Shaikhet L.) A new view on one problem of asymptotic behavior of solutions of delay difference equations. Discrete Dynamics in Nature and Society. 2006. V.2006, Article ID 74043, 16 pages. download
- (Shaikhet L.) About stability of a difference analogue of a nonlinear integro-differential equation of convolution type. Applied Mathematics Letters, 2006. V.19, N.11, p.1216-1221. download
2005
- (Shaikhet L.) Stability of difference analogue of linear mathematical inverted pendulum. Discrete Dynamics in Nature and Society. 2005. V.2005, N.3, p.215-226. download
- (Shaikhet L.) General method of Lyapunov functionals construction in stability investigations of nonlinear stochastic difference equations with continuous time. Special Issue 'Stochastic Dynamics with Delay and Memory'. Stochastics and Dynamics, 2005, V.5, N.2, p.175-188. download
2004
- (Shaikhet L.) Lyapunov functionals construction for stochastic difference second kind Volterra equations with continuous time. Advances in Difference Equations. 2004. V.2004, N.1, p.67-91. download
- (Paternoster B., Shaikhet L.) Application of the general method of Lyapunov functionals construction for difference Volterra equations. Computers and Mathematics with Applications. 2004. V.47, N.8-9, p.1165-1176. download
- (Kolmanovskii V., Shaikhet L.) About some features of general method of Lyapunov functionals construction. Stability and Control: Theory and Applications. 2004. V.6, N.1, p.49-76. download
- (Shaikhet L., Roberts J. ) Stochastic Volterra integro - differential equations: stability and numerical methods. University of Manchester. MCCM. Numerical Analysis Report, No.450, June 2004. 38p. download
- ( Shaikhet L.) About Lyapunov functionals construction for difference equations with continuous time. Applied Mathematics Letters. 2004. V.17, N.8, p.985-991. download
- ( Shaikhet L.) Construction of Lyapunov functionals for Stochastic Difference Equations with Continuous Time. Mathematics and Computers in Simulation. 2004. V.66, N.6, p.509-521. download
2003
- (Kolmanovskii V., Shaikhet L.) About one application of the general method of Lyapunov functionals construction. International Journal of Robust and Nonlinear Control (Special Issue on Time Delay Systems, RNC). 2003. V.13, N.9, p.805-818. download
- (Kolmanovskii V., Shaikhet L.) Some conditions for boundedness of solutions of difference Volterra equations. Applied Mathematics Letters. 2003. V.16, N.6, p.857-862. download
2002
- (Kolmanovskii V., Shaikhet L.) Some peculiarities of the general method of Lyapunov functionals. Applied Mathematics Letters. 2002. V.15, N.3, p.355-360. download
- (Shaikhet L.) Numerical simulation and stability of stochastic systems with Markovian switching. Neural, Parallel and Scientific Computations. 2002. V.10, N.2, p.199-208. download
- (Kolmanovskii V., Shaikhet L.) Construction of Lyapunov functionals for stochastic hereditary systems: a survey of some recent results. Mathematical and Computer Modeling. 2002. V.36, N.6, p.691-716. download
2000
- (Paternoster B., Shaikhet L.) About Stability of Nonlinear Stochastic Difference Equations. Applied Mathematics Letters. 2000. V.13, p.27-32. download
- (Borne P., Kolmanovskii V., Shaikhet L.) Stabilization of inverted pendulum by control with delay. Dynamic Systems and Applications, 2000, V.9, N.4, p.501-514. download
- (Mao X., Shaikhet L.) Delay-dependent stability criteria for stochastic differential delay equations with Markovian switching. Stability and Control: Theory and Applications, 2000, V.3, N.2, p.88-102. download
1999
- (Borne P., Kolmanovskii V., Shaikhet L.) Steady-state solutions of nonlinear model of inverted pendulum. Proceedings of The Third Ukrainian - Scandinavian Conference in Probability Theory and Mathematical Statistics, June 8-12, 1999, Kyiv, Ukraine. download
1998
- (Shaikhet G., Shaikhet L.) Stability of stochastic linear difference equations with varying delay. In Advances in Systems, Signals, Control and Computers (V. Bajic Ed.), ISBN 0-620-23136-X, IAAMSAD and SA branch of the Academy of Nonlinear Sciences, Durban, South Africa, 1998, p. 101-104. download
- (Kolmanovskii V., Shaikhet L.) Riccati equations and stability of stochastic linear systems with distributed delay. In Advances in Systems, Signals, Control and Computers (V. Bajic Ed.), ISBN 0-620-23136-X, IAAMSAD and SA branch of the Academy of Nonlinear Sciences, Durban, South Africa, 1998, p. 97-100. download
- (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"), 1998, V.45, N3-4, p. 269-277. download
- (Shaikhet L.) Stability of predator-prey model with aftereffect by stochastic perturbations. SACTA, Vol. 1, No., 1, 1998, p. 3-11. download
- (Shaikhet L.) Stability of systems of stochastic linear difference equations with varying delays. Proceeding of the Donetsk Colloquium on Probability Theory and Mathematical Statistics dedicated to the 80th Birthday of Josef I. Gikhman (1918-1985). Donetsk, Ukraine, May 24-27, 1998. download
- (Kuchkina N.V., Shaikhet L.E.) Optimal control of Volterra type stochastic difference equations. Computers and Mathematics with Applications (Special Issue "Advances in difference equations II"). 1998. V.36, N.10-12, p.251-259. download
1997
- (Agarwal R.P., Shaikhet L.E.) Linear square optimal control problem for stochastic difference equations with unknown parameters. Mathematical and Computer Modelling. 1997. V.25, N.2, p.3-9. download
- (Kuchkina N.V., Shaikhet L.E.) Optimal control problem for nonlinear stochastic difference second kind Volterra equations. Computers and Mathematics with Applications. 1997. V.34, N.9, p. 65-73. download
- (Kolmanovskii V., Shaikhet L.) Matrix Ricatti equations and stability of stochastic linear systems with non-increasing delays. Functional Differential Equations, 1997, V.4, N.3-4, p.279-293. download
- (Shaikhet L.) Necessary and Sufficient Conditions of Asymptotic Mean Square Stability for Stochastic Linear Difference Equations. Appl. Math. Left. Vol. 10, No. 3, pp. 111-115, 1997. download
1996
- (Shaikhet L.) Stability of Stochastic Hereditary Systems with Markov Switching. Theory of Stoch. Proc. Vol. 2 (18), No. 3-4, pp. 180-184, 1996. download
1995 and earlier
- (Kolmanovskii V., Shaikhet L.) General method of Lyapunov functionals construction for stability investigation of stochastic difference equations. Dynamical Systems and Applications, World Sci. Ser. Appl. Anal., World Sci. Publishing, River Edge, NJ. V.4, 1995, p.397-439. link
- (Shaikhet L.E.) Stability in probability of nonlinear stochastic hereditary systems. Dynamic Systems and Applications 4 (1995) 199-204. download
- (Shaikhet L.E.) Stability in probability of nonlinear stochastic systems with delay. Matematicheskiye zametki. 1995. V.57, N.1, p.142-146 (in Russian). Translated in Mathematical Notes. 1995. V.57, N.1-2, p.103-106. download
- (Shaikhet L.E.) Asymptotic stability of linear stochastic differential equations of neutral type. Matematicheskiye zametki. 1992. V.52, N.2, p.144-147 (in Russian). Translated in Mathematical Notes. 1992. V.52, N.2, p.856-858. download
- (Shaikhet L.E.) Optimal control of certain hyperbolic and integral stochastic equations. Teoriya slutchajnikh protsessov. 1987. V.15, p.110-116 (in Russian). Translated in Journal of Soviet Mathematics. 1991. V.53, N.4, p.457-462. download