Fundamental theorem of state feedback for singular systems

Abstract The limits of state feedback in altering the dynamics of singular systems are studied. A necessary and sufficient condition is given for a list of polynomials to be invariant polynomials of a proper system obtained by state feedback from the singular system. The condition consists of inequalities which involve the controllability indices of the singular system and the degrees of the invariant polynomials. The development is based on the properties of polynomial matrices. A procedure is given for the calculation of a feedback gain which achieves the desired dynamics.