The problems of robust stability and robust stabilization of linear state-space

systems with parameter uncertainties have been extensively studied in the

past decades [25, 209]. Many results on these topics have been proposed.

Among the different approaches that deal with these problems, the methods

based on the concepts of quadratic stability and quadratic stabilizability have

become popular. An uncertain system is quadratically stable if there exists a

fixed Lyapunov function to infer the stability of the uncertain system, while

an uncertain system is quadratically stabilizable if there exists a feedback controller

such that the closed-loop system is quadratically stable. Many results

on quadratic stability and quadratic stabilizability have been reported in both

the continuous and discrete contexts