Optimization Based State Feedback Control Design for Impulse Elimination in Descriptor Systems

This article proposes an algorithm to minimize the Frobenius norm of state feedback gain matrix of a regular, linear time invariant, continuous time descriptor system. The resulting gain matrix ensures that the closed loop system is impulse-free and the associated non singular matrix is well-conditioned. By characterizing a subset of the set of non singular matrices through a linear matrix inequality, the related optimization is formulated as a semi-definite program. Numerical example illustrates the effectiveness of the proposed approach.