Fluid systems are most efficient for fully attached flows, and designers therefore seek to avoid flow separation. Active flow control can help achieve this goal, and closed-loop control offers improved performance at off-design conditions. However, this requires feedback of accurate state estimates to the controller in real time. This motivates a physics-based, state-estimation technique that economically extracts key dynamical features of the flow. This work aims to extract dynamical characteristics of a laminar separation bubble on a flat plate at a chord Reynolds number of 105 using a linear array of unsteady surface pressure measurements. First, Dynamic Mode Decomposition (DMD) is employed on high-dimensional time-resolved PIV velocity and corresponding estimated pressure fields to identify the dynamically relevant spatial structure and temporal characteristics of the separated flow. Then, results are presented of various open-loop control cases using pulse-modulation of a zero-net mass-flux actuator slot located just upstream of separation. Real-time estimates of the dynamical characteristics are provided by performing online DMD on measurements from a linear array of 13 unsteady surface pressure transducers. The results show that this method provides reliable updates of the modal characteristics of the separated flow subject to forcing at a rate much faster than the characteristic time scales of the flow. Therefore, online DMD applied to the surface pressure measurements provides a time-varying linear estimate of the evolution of the controlled flow, thereby enabling closed-loop control.