Spatial-temporal security stability analysis and regulation against different types of attacks on industrial control systems

In this article, reaction-diffusion phenomena are considered in the security risk modeling of industrial control networks represented in the spatial-temporal domain. Different types of cyber-physical attacks, including TDS (time delay switch), FDI (false data injection), and DoS (denial of service), are modeled within a comprehensive parameteric-varying parabolic partial differential state-space structure. A theorem is proposed to ensure that the system is asymptotically stable with prescribed H & INFIN;$$ {H}_{\infty } $$ performance, which guarantees stability regardless of the various types of attacks. Finally, corresponding examples of risk control design against the different threats on industrial control networks are simulated to demonstrate the effectiveness of the results proposed in this article.