Reduced-order filtering for semi-Markovian jump systems against randomly occurring false data injection attacks

Abstract

This paper describes a mode-dependent reduced-order filtering problem for semi-Markovian jump systems with time-varying delay and external disturbance, where the measurement output is vulnerable to randomly occurring false data injection attacks. To facilitate analysis, the attacks are described by a nonlinear function that meets Lipschitz continuity and the possible attack scenarios are represented by a stochastic parameter that follows the Bernoulli distribution. Based on the information from the considered system and reduced-order filter, an augmented filtering system is constructed. Then, a convex optimization problem is formulated by using Lyapunov-Krasovskii stability theory and stochastic analysis. The filter gain matrices are efficiently derived as a result, ensuring that the augmented filtering system is stochastically stable and strictly (Q,S,R)−γ-dissipative. Through numerical examples, the advantages and effectiveness of the developed theoretical findings are clearly demonstrated.