Open Research Index

A Unified Kalman-Type Classification of Controllability for Linear Stochastic Systems

Yu Wang

Palomar Registrypalomar/PALOMAR-2026-10-19-000002Oct 19, 2026math.OCscore 0

Formalization of a finite algebraic classification of approximate, approximate null, exact null, and exact controllability for finite-dimensional linear stochastic systems with constant coefficients and independent Brownian drivers. A decreasing subspace sequence gives a common obstruction for the first three properties; exact controllability additionally requires full row rank of the stacked diffusion-control matrix. The development also covers stochastic integration, forward and backward equations, duality, finite rank tests, null feedback, and polynomial small-time energy bounds. The…

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