Asynchronous secure control for singular nonhomogeneous Markov jump cyber‐physical systems against dual cyber‐attacks

In this article, based on the dynamic event‐triggered transmission protocol, the issue of asynchronous secure control for singular nonhomogeneous Markov jump cyber‐physical systems (CPSs) is studied. The matrix that is governed by the time‐varying transition rates lies in a convex polyhedron. To further degrade the transmission percentage over the network, the dynamic event‐triggered transmission protocol is developed. Besides, owing to the vulnerability of the network, the replay attack and deception attack are both considered, the occurrences of which are modelled by mutual independent random variables satisfying Bernoulli distribution. By constructing a parameter dependent and an auxiliary dynamic variable dependent Lyapunov functional, sufficient conditions of stochastic admissible for singular nonhomogeneous Markov jump CPSs are derived by parameter dependent matrix inequalities, which can be converted into the finite linear matrix inequalities. A numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results.