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arXiv · 2608.21933

Hautus criteria for exact controllability and stabilizability of discrete-time backward-structured stochastic linear systems

Xurun Zuo
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Abstract

This paper studies exact controllability and L2-stabilizability of discrete-time backward-structured stochastic linear systems. For each prescribed finite horizon, equivalent characterizations of exact controllability are established in terms of the controllability Gramian, a Kalman-type rank condition, and the reachable subspace. Exact null controllability without a prescribed horizon is then characterized by a finite-dimensional rank condition, and a Hautus-type criterion is derived using positive semidefinite eigenmatrices of a positive operator. For L2-stabilizability, we establish a stabilizability decomposition and obtain a corresponding Hautus-type spectral criterion. As a byproduct, we show that exact null controllability implies L2-stabilizability. These results provide algebraic and spectral tests for the controllability and stabilizability of the considered systems.

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Xurun Zuo. 2026-08-22. Hautus criteria for exact controllability and stabilizability of discrete-time backward-structured stochastic linear systems. https://arxiv.org/abs/2608.21933

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