About quadratic stabilizability of generalized linear systems

The authors introduce the quadratic stabilizability concept for generalized linear systems. A sufficient and necessary condition for quadratic stabilizability and its associated numerical procedure are given. Then, it is shown that the extension to the uncertain case is not as easy as in the case of a continuous linear system in state-space form. However, a sufficient condition for stabilizability is given. The numerical procedure based on linear programming is derived via a cutting plane technique. Some examples are used to show the usefulness of the approach