\(H_\infty\) fault detection for linear discrete time-varying descriptor systems with missing measurements (Q1723552)

Summary: This paper deals with the problem of \(H_\infty\) fault detection for a class of linear discrete time-varying descriptor systems with missing measurements, and the missing measurements are described by a Bernoulli random binary switching sequence. We first translate the \(H_\infty\) fault detection problem into an indefinite quadratic form problem. Then, a sufficient and necessary condition on the existence of the minimum is derived. Finally, an observer-based \(H_\infty\) fault detection filter is obtained such that the minimum is positive and its parameter matrices are calculated recursively by solving a matrix differential equation. A numerical example is given to demonstrate the efficiency of the proposed method.