Non-fragile control design for stochastic Markov jump system with multiple delays and cyber attacks

Abstract This study inspects the stabilization problem for a class of stochastic Markovian jump systems with multiple delays and cyber attacks by using a non-fragile control law. Notably, the multiple delays which contains both discrete time-varying delays and distributed delays in a single framework. To be precise, non-fragile controller is designed with the intention to handle the issues of gain fluctuations in the control components. In addition to that, the cyber attack scheme is vulnerable to the adversary, which transmits the malicious information to the control signals in an insecure network. The foremost target in this study is to frame a non-fragile control protocol for the addressed stochastic Markov jump systems to authenticate the stochastic stability under the influence of cyber attack. By adopting Lyapunov-Krasovskii functional, a series of adequate criteria is procured in the configuration of linear matrix inequalities to assure the stochastic stability of the addressed Markov jump systems. Based on this criterion, the design procedure for non-fragile controller gains is systematically computed. Ultimately, two numerical examples are used to verify the validity and usefulness of the proposed controller design.