An Input-Output Approach to Structured Stochastic Uncertainty in Continuous Time
For control theorists, this provides a unified stability analysis framework for a broader class of stochastic systems, though the contribution is incremental as it extends existing input-output methods to continuous-time stochastic settings.
This paper characterizes mean-square stability conditions for LTI systems with multiplicative stochastic uncertainties using a purely input-output approach, avoiding state-space realizations and thus covering infinite-dimensional systems and delays. The conditions are expressed via the spectral radius of a matrix operator, with different forms for Itō and Stratonovich interpretations.
We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of 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 state space realizations. This has the advantage of encompassing a wider class of models (such as infinite dimensional systems and systems with delays). The input-output approach leads to uncovering new tools such as stochastic block diagrams that have an intimate connection with the more general Stochastic Integral Equations (SIE), rather than Stochastic Differential Equations (SDE). Various stochastic interpretations are considered, such as Itō and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a matrix operator that takes different forms when different stochastic interpretations are considered.