  We revisit the Thompson sampling algorithm to control an unknown linear
quadratic (LQ) system recently proposed by Ouyang et al (arXiv:1709.04047). The
regret bound of the algorithm was derived under a technical assumption on the
induced norm of the closed loop system. In this technical note, we show that by
making a minor modification in the algorithm (in particular, ensuring that an
episode does not end too soon), this technical assumption on the induced norm
can be replaced by a milder assumption in terms of the spectral radius of the
closed loop system. The modified algorithm has the same Bayesian regret of
$\tilde{\mathcal{O}}(\sqrt{T})$, where $T$ is the time-horizon and the
$\tilde{\mathcal{O}}(\cdot)$ notation hides logarithmic terms in~$T$.
