Quadratic stabilizability of linear uncertain systems in convex-bounded domains

In this paper, a relationship is derived between quadratic stabilizability of linear systems with convex bounded uncertainty domains and the existence of a positive definite solution to a well defined set of Riccati equations. Both continuous and discrete-time models are investigated. For continuous-time systems, the results reported here are compared with the ones provided in the literature, where norm-bounded uncertainty is considered. A numerical example is included.