  While the optimization landscape of policy gradient methods has been recently
investigated for partially observed linear systems in terms of both static
output feedback and dynamical controllers, they only provide convergence
guarantees to stationary points. In this paper, we propose a new policy
parameterization for partially observed linear systems, using a past
input-output trajectory of finite length as feedback. We show that the solution
set to the parameterized optimization problem is a matrix space, which is
invariant to similarity transformation. By proving a gradient dominance
property, we show the global convergence of policy gradient methods. Moreover,
we observe that the gradient is orthogonal to the solution set, revealing an
explicit relation between the resulting solution and the initial policy.
Finally, we perform simulations to validate our theoretical results.
