$\ell_{1}/\ell_{-}$ Filter-Based Fault Detection for Positive Markov Jump Linear Systems With Time Delay

The purpose of this paper is to design a positive fault detection filter for positive Markov jump linear systems (MJLSs) using ℓ
₁
and ℓ
_-
performance indices, which represent respectively, robustness and fault sensitivity. First, by converting the MJLS to an associated deterministic system, sufficient conditions are derived for the positivity, stochastic stability and ℓ
₁
/ℓ_ performance of an augmented system consisting of the original system and the fault detection filter. Then an iterative linear programming (LP) algorithm is provided to solve these bilinear conditions, with two numerical examples presented to show the superiority of the developed approach over the existing ones.