Data-Driven Pole Placement in LMI Regions with Robustness Guarantees

This paper proposes a data-driven methodology to place the closed-loop poles in desired convex regions in the complex plane with sufficient robustness constraints. We considered the system state and input matrices unknown and only used the measurements of system trajectory. The closed-loop pole placement problem in the linear matrix inequality (LMI) regions is considered a classic robust control problem; however, that requires knowledge about the state and input matrices of the linear system. We bring in ideas from the behavioral system theory and persistency of excitation condition-based fundamental lemma to develop a data-driven counterpart that satisfies multiple closed-loop robustness specifications, such as D-stability and mixed H-2/H-infinity performance specifications. We provide solutions based on the availability of the disturbance input, both in the controlled and fully uncertain environment, leading to data-driven semi-definite programs (SDPs) with sufficient guarantees. We validate the theoretical results with numerical simulations on a third-order dynamic system.