Data-Driven Output Feedback Control for Unknown Piecewise Affine Systems

This article investigates data-driven output feedback control of unknown piecewise affine (PWA) systems. The objective is to design controllers that exponentially stabilize PWA systems without requiring explicit subsystem models. A data-dependent representation of the PWA system is first constructed using either input-state-output (ISO) or input-output (IO) data, depending on the availability of state measurements. Based on this representation, a piecewise output feedback controller is synthesized using the multiple Lyapunov function approach. Three key challenges are addressed. First, partition information is incorporated into the controller design to reduce conservativeness. Second, multiple datasets are employed to accommodate the switching nature of PWA systems, avoiding the need for a single long persistently exciting (PE) trajectory. Third, in the IO-data case, a left coprime condition is introduced to guarantee controllability of the constructed system. The effectiveness of the proposed method is demonstrated through three examples.