Stability analysis for stochastic differential equations with infinite Markovian switchings

This paper is concerned with stability analysis of linear Itô stochastic differential equations with countably infinite Markovian switchings. A spectral criterion is proposed for exponential stability of the considered models. By means of the established spectral criterion, the relationship between exponential stability and stochastic (L2L2) stability is clarified. Moreover, under the disturbance of random signals with finite energy, a sufficient condition is presented for L2L2 input–output stability of the perturbed stochastic differential equations.