Quadratic stabilization of distributed parameter systems with norm-bounded time-varying uncertainty

This note focuses on the study of robust $H_\infty$ control design for a kind of distributed parameter systems in which time-varying norm-bounded uncertainty enters the state and input operators. Through a fixed Lyapunov function, we present a state feedback control which stabilizes the plant and guarantees an $H_\infty$ norm bound on disturbance attenuation for all admissible uncertainties. In the process, we generalize some known results for finite dimensional linear systems