Computational methods for MIMO flat linear systems: Flat output characterization, test and tracking control

This paper is concerned with the study of flat outputs for multiple-input-multiple-output (MIMO) controllable linear time-invariant discrete- and continuous-time systems in state-space representation. Leveraging the equivalence of flatness to an estimation-theoretic system property known as strong observability, a quick computational test is developed for ascertaining if an output candidate is flat and the subspace of flat outputs can be constructively characterized. Moreover, we propose a computational method to find differentially (continuous-time), as well as non-causal and causal difference (discrete-time) flat outputs via a system transformation into a special control canonical form. Finally, design principles for flatness-based trajectory planning and tracking control for discrete-time systems are presented, which to our best knowledge, have yet to be successfully demonstrated.