Linear Matrix Inequalities in Fault Detection Filter Design for Linear Ostensible Metzler Systems

The article deals with the properties of fault detection filters when applying their structure to a class of linear, continuous-time systems, with dynamics being specified by the system matrix of the ostensible Metzler structure. The proposed solution is reduced to the use of diagonal stabilization in the synthesis of the state observer and uses the decomposition of the ostensible Metzler matrix. The approach creates a unified framework that covers the compactness of parametric constraints on Metzler matrices and their quadratic stability. Due to the complexity of such constraints, the design conditions are formulated using sharp linear matrix inequalities. For potential application in network control structures, the problem is formulated and solved for linear discrete-time ostensible positive systems. Finally, a linearized model of the B747-100/200 aircraft is used to validate the proposed method. The numerical solution and simulation results show that the proposed approach provides superior sensitivity of the fault detection filter in detecting faults, compared to synthesis methods that do not guarantee the positivity of the filter gain.