General solution to diagonal model matching control of multiple-output-delay systems and its applications in adaptive scheme

This paper mainly studies the model matching problem of multiple-output-delay systems in which the reference model is assigned to a diagonal transfer function matrix. A new model matching controller structure is first developed, and then, it is shown that the controller is feasible if and only if the sets of Diophantine equations have common solutions. The obtained controller allows a parametric representation, which shows that an adaptive scheme can be used to tolerate parameter variations in the plants. The resulting adaptive law can guarantee the global stability of the closed-loop systems and the convergence of the output error.