Some Generalization of the Method of Stability Investigation for Nonlinear Stochastic Delay Differential Equations

Abstract

It is known that the method of Lyapunov functionals is a powerful method of stability investigation for functional differential equations. Here, it is shown how the previously proposed method of stability investigation for nonlinear stochastic differential equations with delay and a high order of nonlinearity can be extended to nonlinear mathematical models of a much more general form. An important feature is the combination of the method of Lyapunov functionals with the method of Linear Matrix Inequalities (LMIs). Some examples of applications of the proposed method of stability research to known mathematical models are given.

Keywords

• stability of equilibria
• nonlinear delay differential equations
• stochastic perturbations
• asymptotic mean square stability
• stability in probability
• Linear Matrix Inequality (LMI)