Multiplier - Based Robust H 1 Estimationwith Applications to Robust Fault Detectionby

This paper uses the Popov-Tsypkin multiplier (which has intimate connections to mixed struc-tured singular value theory) to design robust H 1 estimators and considers the application of the robust H 1 estimator to robust fault detection for uncertain linear discrete-time systems. The key to estimator-based robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs which in turn requires the design of robust estima-tors. The robust H 1 estimation problem is formulated as a Riccati equation feasibility problem in which a cost function is minimized subject to a Riccati equation constraint. A quasi-Newton BFGS continuation algorithm is developed to solve the minimization problem. In particular, the correction steps of the continuation algorithm are performed by using the BFGS inverse Hessian update. The algorithm is initialized with a H 1 estimator corresponding to the nominal system. The initializing multiplier matrices are obtained by solving a linear matrix inequality. The robust H 1 estimator obtained is then applied to the robust fault detection of dynamic systems. It is shown that robust fault detection mechanisms based on robust H 1 estimation methodology proposed in this paper can reduce false alarm rate. A numerical example is presented to illustrate the design algorithms.