Abstract
This paper presents necessary and sufficient conditions for a linear descriptor system to be quadratically stabilizable via linear feedback control. Uncertainties in the system are structured and norm-bounded. It is assumed that the system has no impulsive mode and the coefficient matrix for the derivative of the descriptor variable has no uncertainty. Quadratic stabilizability is defined by introducing a positive semidefinite quadratic function which is, however, positive definite for dynamic behaviors of the descriptor variable. The stabilizability conditions are described in terms of the existence of certain solutions of a generalized algebraic Riccati equation.
