Proportional Integral Observer‐Based Secured Resilient Control for Nonlinear Semi‐Markov Jump Cyber‐Physical Systems Under Multiple Cyberattacks

This research focuses on the state estimation based stabilization of nonlinear semi‐Markov jump cyber‐physical systems that are exposed to external disturbances, multiple cyberattacks, time‐varying delay and gain fluctuations. A proportional integral observer is constructed to reconstruct the immeasurable system states. The stabilization issue is addressed through the design of an appropriate resilient control that can withstand multiple cyberattacks, namely denial‐of‐service and deception attacks. In particular, the occurrence of multiple cyberattacks is characterized by two independent Bernoulli‐distributed random variables. Moreover, a mode dependent Lyapunov–Krasovskii functional is employed along with integral inequalities to derive a set of sufficient conditions in the form of linear matrix inequalities, which ensures stochastic stability and ‐ dissipativity of the addressed system regardless of multiple cyberattacks. Subsequently, the resulting conditions are solved to compute the values of the observer and controller gain matrices. Eventually, two numerical examples are provided to validate the theoretical outcomes.