On Partial <i>C</i> ‐ and <i>S</i> ‐Controllability Results for Semilinear Stochastic Systems

This article investigates the concepts of partial C ‐ and S ‐controllability for semilinear control systems that are disturbed by white noise. For these types of systems, it can be beneficial to study the deterministic and stochastic parts of the system separately, using a separation principle approach. This allows the deterministic and stochastic aspects of the system’s controllability properties to be interpreted independently, which can provide useful insights. Indeed, the partial complete null controllability of the deterministic semilinear system, along with a suitable Lipschitz condition on the nonlinear term, combined with the partial C (respectively, S )‐controllability of the associated stochastic linear system, are sufficient conditions for establishing the partial C (respectively, S )‐controllability of the overall semilinear stochastic system in a separable Hilbert space. An illustrative example is presented to highlight the practical relevance of the theoretical outcomes.