SUMMARYGeneral recent techniques in fault detection and isolation (FDI) are based on H ∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation-based design methods. This article presents an LMI formulation to design full-order and reduced-order robust H ∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full-order filter, which may be solved via recently developed LMI optimization techniques. For the reduced-order FDI filter, the inequalities include a non-convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design.

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Microcystin-LR (MC-LR) is the most frequent and most toxic microcystin identified. This natural toxin has multiple features, including inhibitor of protein phosphatases 1 and 2A, inducer of oxidative stress, as well as, tumor initiator and promoter. One unique character of MC-LR is this chemical can accumulate into liver after contacting and lead to severe damage to hepatocytes, such as apoptosis. Fas receptor (Fas) and Fas ligand (FasL) system is a critical signaling system initiating apoptosis. In current study, we explored whether MC-LR could induce Fas and FasL expression in HepG2 cells, a well used in vitro model for the study of human hepatocytes. The data showed MC-LR induced Fas and FasL expression, at both mRNA and protein levels. We also found MC-LR induced apoptosis at the same incubation condition at which it induced Fas and FasL expression. The data also revealed MC-LR promoted nuclear translocation and activation of p65 subunit of NF-κB. By applying siRNA to knock down p65 in HepG2 cells, we successfully impaired the activation of NF-κB by MC-LR. In these p65 knockdown cells, we also observed significant reduction of MC-LR-induced Fas expression, FasL expression, and apoptosis. These findings demonstrate that the NF-κB mediates the induction of Fas and FasL as well as cellular apoptosis by MC-LR in HepG2 cells. The results bring important information for understanding how MC-LR induces apoptosis in hepatocytes.

In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]