  This paper studies online solutions for regret-optimal control in partially
observable systems over an infinite-horizon. Regret-optimal control aims to
minimize the difference in LQR cost between causal and non-causal controllers
while considering the worst-case regret across all $\ell_2$-norm-bounded
disturbance and measurement sequences. Building on ideas from Sabag et al.,
2023, on the the full-information setting, our work extends the framework to
the scenario of partial observability (measurement-feedback). We derive an
explicit state-space solution when the non-causal solution is the one that
minimizes the $\mathcal H_2$ criterion, and demonstrate its practical utility
on several practical examples. These results underscore the framework's
significant relevance and applicability in real-world systems.
