Robust H ∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement

In this paper, a robust H ∞ control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise/piecewise control and pointwise/piecewise measurement has been investigated via the robust H ∞ feedback compensator design approach. A unified Lyapunov direct approach is proposed in consideration of the pointwise/piecewise control and point/piecewise measurement based on the distributions of the actuators and sensors. A new type of Luenberger observer is developed on the continuous interval of space domain to track the state of the system, and an H ∞ performance constraint with prescribed H ∞ attenuation levels is proposed in this paper. By utilizing Lyapunov technique, mathematical inequalities, and integration theory, a sufficient condition based on LMI for the exponential stability of the corresponding closed-loop coupled system under an H ∞ performance constraint is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.