Transformation of Multi-Input Linear Time-Varying Systems into High-Order Fully Actuated Systems

For a single-input linear time-varying (LTV) system, it can be transformed into a standard high-order fully actuated system (HOFAS) if and only if its controllability matrix, as defined by the Silverman criterion, is nonsingular for all time. However, the scenario becomes much more complex for the multi-input LTV system. This note explores the transformation of a multi-input LTV system to the HOFAS model. For a lexicographically fixed LTV system, the transformation to the HOFAS model can be carried out directly. For a non-lexicographically fixed LTV system, an auxiliary system is introduced to obtain an extended LTV system that is lexicographically fixed, which is then transformed into the HOFAS model.