Infinite-eigenvalue assignment for descriptor systems via state variable feedback

Firstly, the parametric form of the variable K in the matrix pencil A+BK was given, such that when K varied in R^n×n and A was nonsingular, A+BK was nonsingular. Based on it and matrix equation theory, a sufficient and necessary condition was obtained to make the infinite-eigenvalue assignment for descriptor systems solvable by state variable feedback, that was to find K such that the close-loop descriptor system (E, A+BK) only has infinite eigenvalues. Finally, an algorithm to solve the problem was presented, and a numerical example was included to demonstrate the proposed algorithm.