Controllability analysis is concerned with determining the limitations on achievable dynamic performance. This paper proposes ℒ1-optimisation as a useful linear controllability analysis technique for process applications. Performance requirements are expressed in terms of minimising the maximum deviation of selected variables over time. The analysis problem is solved as a linear program with constraints that capture fundamental process limitations to achievable control performance. Key characteristics of the solution method are presented. Some suggestions for how to handle limitations of the method due to the nature of the disturbance and controller descriptions are discussed. To demonstrate the ℒ₁-optimisation method it is applied to an industrial case study. Finally an adaptation of the ℒ1-optimisation framework to incorporate economic performance objectives is presented.