Input–output finite-time robust stabilisation of distributed parameter cyber-physical systems with deception attacks

In this paper, we study the state estimation and input–output finite-time (IO-FT) stabilisation issues for cyber-physical distributed parameter systems (CPDPSs) designed by parabolic partial differential equations. More precisely, to reconstruct the immeasurable states of the addressed CPDPSs, a proportional-integral (PI) observer is implemented since the system states are not always readily measurable. Furthermore, the stability analysis is investigated for CPDPSs in the presence of actuator failures, deception assaults, external disturbances and linear fractional uncertainties. Further, a PI observer-based secured quantised reliable controller is designed to ensure the IO-FT stability of the resulting closed-loop system. Moreover, to reduce the burden on the communication medium, the control input data is quantised before transmission by employing logarithmic quantisers. In the meantime, the deception attacks are assumed to possess a stochastic nature which follows Bernoulli distribution. Besides, by utilising Lyapunov stability theory and integral inequality, a set of adequate conditions is obtained for achieving the required result of the undertaken system. Furthermore, the resulting stability criteria are expressed in the form of linear matrix inequalities, which can be solved using the MATLAB software. Eventually, two numerical examples with simulation results are provided to validate the efficacy of the designed controller.