Finite-Frequency Fault Detection Filter Design for Networked Nonlinear Systems With Medium Access Constraints

In this paper, the finite-frequency fault detection filter design problem is investigated for a class of networked nonlinear systems subject to medium access constraints. The nonlinear system is modeled by Takagi–Sugeno (T–S) fuzzy affine dynamic models, and only one node that includes partial measured information can gain access to the shared transmission medium according to the allocated access probability. Within the stochastic $\scr{H}\_\;/\scr{H}_\infty$ filtering framework, an admissible filter is designed such that, in the finite-frequency domain, the filtering error system is stochastically stable and the fault can be detected using partially available measurements. First, by integrating with S-procedure, the generalized Kalman–Yakubovic–Popov (KYP) lemma is further developed to obtain sufficient conditions guaranteeing the desired finite-frequency performance of the filtering error system. Then, by applying piecewise quadratic Lyapunov functions (PQLFs), Projection lemma, and some con-vexification techniques, the filter design approach is proposed for the constrained networked nonlinear system. It is shown that the filter design problem can be addressed by solving a set of linear matrix inequalities (LMIs). Simulation studies are finally given to illustrate the effectiveness of the proposed design approach.