Sampled-data distributed H∞ control of a class of 1-D parabolic systems under spatially point measurements

This paper considers the sampled-data distributed H∞ control problem for 1-D semilinear transport reaction equations with external disturbances. It is assumed that a finite number of point spatial state measurements are available. A Razumikhin-type approach is developed for stability and L2-gain analysis of the closed-loop system. In contrast to Halanay׳s inequality based approach, the proposed Razumikhin-type approach not only provides a subtle decay estimate of the selected Lyapunov functional, but also guarantees the H∞ performance index to be negative if certain conditions are satisfied. By introducing a time-dependent Lyapunov functional combined with the use of Wirtinger׳s inequality, sufficient conditions for the internal exponential stability and finite L2-gain are derived in terms of linear matrix inequalities. The obtained conditions establish a quantitative relation among the upper bounds on the spatial sampling intervals and the time sampling intervals, and L2-gain. Two numerical examples are provided to illustrate the usefulness of the proposed theoretical results.