By Kallenrode

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**Extra resources for A new approach to linear filtering and prediction problems**

**Example text**

2, thus the proof is concluded. 7) and present a method on how to construct it. 2. 3 H∞ Fault Detection Filter Design 27 ϕ11 = T P1i P2i RT Ai + ρ B f iCi A f i R + RT S + W T ϕ = , − , T 15 T W + ST W + W T P2i P3i S T Ai + ρ B f i C i A f i ϕ16 = P1i P2i RT Bω i + ρ B f i E i R + RT S + W T , ϕ22 = − , T T S Bω i + ρ B f i E i W + ST W + W T P2i P3i ϕ25 = hB f i E i hB f iCi 0 , ϕ26 = , ϕ35 = ρ D f iCi − CW C f i , hB f i E i 0 0 ϕ36 = ρ D f i E i − DW , ϕ45 = hD f iCi 0 , ϕ46 = hD f i E i , ϕ55 = −(1 − α ) P1i P2i P1i P2i A 0 , ϕ¯ 55 = −(1 + β ) T , Ai = W , T 0 Ai P2i P3i P2i P3i C i = 0 Ci , Bω i = 0 0 BW , E i = Eui Edi Ff i , Bui Bdi G f i CW = CW 0 , DW = 0 0 DW .

6. By combining the available stability theory and ADT technique, FD filter design for discrete-time switched systems has been exploited. , ρ = 1. 4 A Reluctance Motor Example Consider a multi-phase switched reluctance motor (SRM) system investigated in [56], whose switched modeling was done in [40]. 02, the discrete-time model is obtained as xk+1 = A(σk )xk + Bu (σk )uk + Bd (σk )dk yk = C(σk )xk + Eu (σk )uk + Ed (σk )dk the state variables are chosen as x1 (t) = θm and x2 (t) = ωm , where θm and ωm denote the angular position and velocity of the motors, separately.

1 Fault detection filter with data loss where xk ∈ Rn is the state, uk ∈ Rm , dk ∈ R p , and fk ∈ Rl are the control input, unknown input, and the fault respectively, which belong to l2 [0, ∞). σk is a piecewise constant function of time, called a switching signal, which takes its values in the finite set ψ = {1, · · · , N}, N > 1 is the number of subsystems. At an arbitrary discrete time k, σk is dependent on time k or state xk , or both, or other switching rules. 3) where yk ∈ Rq is the output, yck ∈ Rq is the measured output.