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We propose an extension of the input-output feedback linearization for aclass of multivariate systems that are not input-output linearizable in aclassical manner. The key observation is that the usual input-outputlinearization problem can be interpreted as the problem of solving simultaneouslinear equations associated with the input gain matrix: thus, even at pointswhere the input gain matrix becomes singular, it is still possible to solve apart of linear equations, by which a subset of input-output relations is madelinear or close to be linear. Based on this observation, we adopt the taskpriority-based approach in the input-output linearization problem. First, wegeneralize the classical Byrnes-Isidori normal form to a prioritized normalform having a triangular structure, so that the singularity of a subblock ofthe input gain matrix related to lower-priority tasks does not directlypropagate to higher-priority tasks. Next, we present a prioritized input-outputlinearization via the multi-objective optimization with the lexicographicalordering, resulting in a prioritized semilinear form that establishes inputoutput relations whose subset with higher priority is linear or close to belinear. Finally, Lyapunov analysis on ultimate boundedness and task achievementis provided, particularly when the proposed prioritized input-outputlinearization is applied to the output tracking problem. This work introduces anew control framework for complex systems having critical and noncriticalcontrol issues, by assigning higher priority to the critical ones.

Input-Output Feedback Linearization Preserving Task Priority for Multivariate Nonlinear Systems Having Singular Input Gain Matrix