Partial Stabilization of Descriptor Systems Using Spectral Projectors

We consider the stabilization problem for large-scale linear descriptor systems in continuousand discrete-time. We suggest a partial stabilization algorithm which preserves stable poles of the system while the unstable ones are moved to the left half plane using state feedback. Our algorithm involves the matrix pencil disk function method to separate the finite from the infinite generalized eigenvalues and the stable from the unstable eigenvalues. In order to stabilize the unstable poles, either the generalized Bass algorithm or an algebraic Bernoulli equation can be used. Some numerical examples demonstrate the behavior of our algorithm.