Control Design for Cyber-Physical Uncertain Systems Under Unreliable Markovian Network Susceptible to Denial-of-Service Attacks

This brief presents new conditions to design mode-dependent state-feedback control gains that guarantee the stochastic stability of uncertain cyber-physical systems (CPS) subject to Denial of Service (DoS) attacks and transmission failures due to an unreliable network. A network model is proposed after a non-homogeneous Markov chain whose transition probability matrix contains uncertain and unknown probabilities modeled by time-varying parameters. Each mode of the stochastic CPS may represent i) successful transmission; ii) transmission failure; or iii) DoS attacks. The conditions are presented in the form of parameter-dependent linear matrix inequalities, that allow the design of mode-dependent gains to stabilize the system under DoS attacks and transmission failures. A numerical example is provided to assess the efficacy of the method.