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 in this paper. 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 will indicate in this paper that for generalized state-space systems the corresponding solutions are not positive definite any more.