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The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control. However, most of the existing literature only considers the optimization landscape for static full-state or output feedback policies (controllers). In this article, we investigate the more challenging case of dynamic output-feedback policies for linear quadratic regulation (abbreviated as dLQR ), which is prevalent in practice but has a rather complicated optimization landscape. We first show how the dLQR cost varies with the coordinate transformation of the dynamic controller, and then, derive the optimal transformation for a given observable stabilizing controller. One of our core results is the uniqueness of the stationary point of dLQR when it is observable, which provides an …