Normal Forms of Linear Time-Varying Systems With Applications to Output-Feedback Stabilization and Tracking

This article examines the normal form of a multiple-input-multiple-output (MIMO) linear time-varying (LTV) system. It explores the transformation of such a system into its normal form using an LTV transformation, if it possesses a general relative degree that may not be uniform (strict). Based on the obtained normal form, the internal and external dynamics as well as the inverse system of the LTV system are investigated. Additionally, the zero dynamics can be effectively parameterized. Moreover, by employing the derived LTV normal form, the proportional-derivative output-feedback stabilization and output tracking problems are resolved. Finally, an illustrative example is presented to showcase the effectiveness of the proposed controllers.