This note focuses on the study of robust H-sub-infinity 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-sub-infinity norm bound on disturbance attenuation for all admissible uncertainties. In the process, we generalize some known results for finite dimensional linear systems.

The L^{P} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^{P} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a...