Stabilizing LTI Systems under Partial Observability: Sample Complexity and Fundamental Limits

We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, the state-of-the-art approaches leverage an unstable/stable subspace decomposition to achieve sample complexity that depends only on the number of unstable modes, independent of the dimension of the system state. However, it remains open whether such sample complexity can be achieved for partially observable systems because such systems do not admit a uniquely identifiable unstable subspace. In this paper, we propose LTS-P, a novel technique that leverages compressed singular value decomposition (SVD) on the ”lifted” Hankel matrix to estimate the unstable subsystem up to an unknown transformation. Then, we design a stabilizing controller that integrates a robust stabilizing controller for the unstable mode and a small-gain-type assumption on the stable subspace. We show that LTS-P achieves state-of-the-art, dimension-free sample complexity that scales only with the number of unstable modes. This substantially reduces data requirements for stabilizing high-dimensional systems, particularly those dominated by stable dynamics.