Finite-time passivity of reaction-diffusion systems with boundary input-output

Finite-time passivity (FTP) is investigated for reaction-diffusion systems (RDSs) that are subject to input-output situated on the boundary. By employing the Lyapunov functional approach in conjunction with various inequality techniques, sufficient conditions are derived for FTP, finite-time input strict passivity and finite-time output strict passivity, respectively. Moreover, the obtained theoretical result demonstrates that FTP implies finite-time stability when systems are not subject to external input. Furthermore, when RDSs are subject to nonlinear uncertainties perturbations, robustly FTP is also investigated and corresponding sufficient conditions are established under the designed controller, indicating that the boundary controller exhibits insensitivity to structural uncertainties to some extent. Finally, under an anti-angiogenic therapy framework, a tumor growth model is adopted to show the validity with boundary nutrient input.