Design of fault-tolerant non-fragile control for parabolic PDE systems with semi-Markov jump: the finite-time case

This study looks into the problem of non-fragile control design for PDE systems in the presence of Neumann-type boundary conditions. In particular, the considered PDE is a parabolic type having semi-Markov jump and is subject to parametric uncertainties and external disturbances. The primary objective of this study is to provide a fault-tolerant non-fragile control protocol that ensures the targeted stabilisation of the system despite gain variations and actuator faults. Moreover, the impact of external disturbances is minimised by employing mixed $ H_{\infty } $ H∞ and passivity performance. After that, adequate criteria are established in the framework of linear matrix inequalities through the construction of a proper Lyapunov function together with the employment of integral-based Wirtinger's inequality such that it ensures the accomplishment of finite-time boundedness with a satisfactory performance level for the closed-loop system. Consequently, the explicit configuration of the developed controller gain matrices is computed, which is obtained by solving the developed criteria. Finally, to show the effectiveness of the devised control approach, simulation results with numerical examples are made available.