Stabilization by variable-delay feedback control for highly nonlinear hybrid stochastic differential delay equations

Abstract

We consider a hybrid SDE (stochastic differential equation) with variable delays, which is unstable and its coefficients satisfy some polynomial growth conditions. We want to find a variable-delays feedback control such that the controlled hybrid SDE with variable delay becomes stable. We establish some novel stability criteria of the controlled SDE with variable delays. Our results improve the existing results from hybrid SDEs with constant-delays to hybrid SDEs with variable-delays. Finally, an example is given to confirm our results.