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We consider the continuous-time setting of linear time-invariant (LTI)systems in feedback with multiplicative stochastic uncertainties. The objectiveof the paper is to characterize the conditions of Mean-Square Stability (MSS)using a purely input-output approach, i.e. without having to resort to statespace realizations. This has the advantage of encompassing a wider class ofmodels (such as infinite dimensional systems and systems with delays). Theinput-output approach leads to uncovering new tools such as stochastic blockdiagrams that have an intimate connection with the more general StochasticIntegral Equations (SIE), rather than Stochastic Differential Equations (SDE).Various stochastic interpretations are considered, such as It\=o andStratonovich, and block diagram conversion schemes between differentinterpretations are devised. The MSS conditions are given in terms of thespectral radius of a matrix operator that takes different forms when differentstochastic interpretations are considered.

An Input-Output Approach to Structured Stochastic Uncertainty in Continuous Time