Eigenvalue assignment inside a disk for generalized state-space systems

The problem of eigenvalue assignment inside a disk for generalized state-space systems is investigated. A necessary and sufficient condition, formulated in the linear matrix inequality form, for eigenvalue clustering inside a specified disk is derived. Then, based on the condition, a state feedback gain is synthesized to ensure not only the closed-loop system is regular and impulse-free but all its finite eigenvalues lie in a specified open disk. For standard state-space systems, the above same problems are dealt with by solving the Lyapunov equation and the Riccati equation whose solutions are positive definite. However, we indicate that for generalized state-space systems the corresponding solutions are not positive definite any more