Output Regulation Problem for Descriptor Switched Systems via the Full-Information Feedback Controller*

In this study, we address the output regulation problem (ORP) for descriptor switched systems through the full-information feedback controller. The analysis begins by ensuring the closed-loop system's regularity and impulse-freeness via a restricted system equivalent transformation. Through the mode-dependent state coordinate transformation, the problem is then recast as a stabilization problem for descriptor switched systems without disturbances. Then relaxation variables are introduced and the average dwell time (ADT) switching is employed to obtain the solvable conditions, which include regulator equations and matrix inequalities. Furthermore, we apply the matrix decoupling techniques to derive less conservative linear matrix inequality (LMI) conditions that guarantee the existence of full-information feedback controllers, and the controller design methodologies are developed as well. Finally, an illustrative example is provided to validate the proposed approaches.