This paper deals with problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems. A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices. Different from the case of linear time invariant systems, the parity space-based residual generator for a Markovian jump system cannot be designed...

The representation given in Example 3 has an interesting property. The set of matrices {ρ(e), ρ(g)} have common invariant subspaces (other than the trivial ones, namely (0, 0) and C). Indeed, we can eas­ ily verify that the (orthogonal) one­dimensional subspaces given by (t, t) and (t, −t) are invariant under the action of these matrices. Therefore, the restriction of ρ to those subspaces also ...

In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

Invariant coordinate selection (ICS ) has recently been introduced by Tyler et al. (2008) as a method for exploring multivariate data. It includes as shown in Oja et al. (2006) as a special case a method for recovering the unmixing matrix in independent components analysis (ICA). It also serves as a basis for classes of multivariate nonparametric tests. The aim of this paper is to briefly expla...