Intermittent distributed control for a class of nonlinear reaction-diffusion systems with spatial point measurements

This paper addresses the intermittent distributed stabilization problems of a class of nonlinear reaction-diffusion systems, where the state measurements are available at a finite number of sampling spatial points. By developing piecewise switching-time-dependent Lyapunov function methods combined with the descriptor system approach, L2-norm and H1-norm stability criteria are established, respectively. For the case of Dirichlet boundary condition, it is shown that the H1-norm stability implies the pointwise-in-space stability. The obtained stability conditions establish a quantitative relationship among the upper bound of the spatial sampling intervals, control width, and rest width. In the framework of linear matrix inequalities, sufficient conditions for the existence of intermittent distributed static output-feedback controllers are derived. A comparison between the two stability criteria is given by means of a numerical example.