ON THE SINGULAR TRACKING PROBLEM

In this paper we continue the analysis of the problem of output tracking in the presence of singularities, whose study was begun by R. Hirschorn and J. Davis. We introduce further structure which is important in quantifying the multiplicity and smoothness of solutions to the problem. The paper is motivated by the analysis of those singular ordinary differential equations whose structure ultimately governs solutions to the singular tracking problem. In the particular case of time-varying linear systems, it is shown how the structure of their solutions in the case of regular and irregular singularities affects solutions to the tracking problem. Less specific results are also obtained in the full nonlinear case.