A controller design based on function observer for singular linear systems : Time and frequency domains approaches

This paper proposes both time and frequency domain design of a controller based on function reduced order observer for linear time-invariant multivariable singular systems where measurements are affected by disturbances. The order of this observer controller is equal to the dimension of the control input and the control gain is designed using H_∞ techniques. The time procedure design is based on the unbiasedness of the estimation error using a Sylvester equation; then a new method to avoid the time derivative of the disturbance in the observation error is proposed and the problem is solved by means of Linear Matrix Inequalities (LMIs). The frequency domain procedure design is derived from time domain results, where we propose some suitable Matrix Fractions Descriptions (MFDs) and mainly, a factorization approach permits to give a polynomial parametrization of the reduced order observer-based controller.