A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift

Abstract

Mean-square stability analysis of linear stochastic differential systems obtained perturbing ordinary systems by linear terms driven by independent Wiener processes is investigated. The so obtained stochastic regions are contractions of the asymptotic stability domain of the linear ordinary system. In this work, the mean-square stability regions exact shape is provided by means of necessary and sufficient conditions in terms of the eigenvalues of the drift and the intensities of the noises. Special attention is paid to how different structures of the perturbation affect the mean-square stability of systems with non-normal drifts. In each case, the obtained explicit stability condition reveals the role played by the parameter that controls the non-normality.