Three singularities in control problems

We consider linear-quadratic optimal feedback design for singular singular- perturbed systems (SSPS). In these problems we run into various types of si ngularities. The first one is connected with small parameters in the coeffi cients of the derivatives in the differential equations. The second singula rity shows up if the reduced DAE system has index > 1. And the last singula rity is due to singularity fo the weighting matrix in the performance crite rion. Tikhonov-Levinson theory, standard time-scale modeling and Riccati eq uation approach to the control problem do not apply for the SSPS. Therefore in the case of design of a linear-quadratic optimal control the related di fficulties have to be considered. We report interactions between singularit ies, and explain the different approaches to the optimal control design.