Preview control for impulse-free continuous-time descriptor systems

This paper studies the preview control problem of impulse-free linear continuous-time descriptor systems. The system is first decomposed into a normal system (i.e., slow subsystem) and an algebraic equation set, by restricted equivalent linear transformation. Then, applying the method of preview control theory to the slow subsystem, by taking derivatives on both the error vector and the state function, and with the error vector being a part of the new state vector, the augmented system is constructed and the tracking problem is transformed into a regulation problem. According to preview control theory, the controller of the augmented system can be obtained and the control input of the original descriptor system with preview function can be acquired by integrating on the controller of the augmented system. Both the stabilisability and detectability of the augmented system are discussed. Numerical simulation verifies the presented results.