Robust Fault Detection in a Mixed Η₂/Η_α Setting: The Discrete - Time Case

Influence of Sampling Period on a Class of Optimal Fault-Detection Performance

“…Lemma 2: [18] Given SD system described by (8)-(10), residual generator (12). Then the optimal observer parameters L T ; W T can be obtained by solving an H1=H1-type optimization problem max L ;W J 1;T = max…”

“…Thus, a residual signal ro can be generated by the following residual generator with constant free parameters L and Wx (k + 1) = AT;x(k)+BT;u(k)+L (y(k)0ỹ(k)) y (k) = C x (k)+D u (k) r o (k) = W (y (k)0ỹ (k)) : (19) is identical with the -step lifting of the residual signal r generated by (12), ifx (0) x ((k + 1)) = A T;x (k) + B T; u (k) + L T; (y (k) 0ŷ (k)) y (k) = C x (k) + D u (k) + Q (y (k) 0ŷ (k)) r(k) = WT; (y(k) 0ŷ(k)) (22) whereŷ (k) =ŷ (0)). It leads to y (0) 0ỹ (0) = (I + Q)(y (0) 0ŷ (0)) ) r o (0) = r (0);x (1) =x():…”

“…According to Lemma 2-5, for SD system (8)-(10) with sampling period T , we can generate the residual signal either by (12) or by (19). Both schemes achieve the same optimal H1=H1 index and there is a one-to-one relationship between the optimal parameters of these two schemes.…”

“…Both schemes achieve the same optimal H1=H1 index and there is a one-to-one relationship between the optimal parameters of these two schemes. That means also using time-varying parameters LT (k); WT (k) in residual generator (12) will not improve the optimal H1=H1 index.…”

“…It leads to a wellestablished framework of FDI approaches for linear systems [3], [8], [10], [12], [15], [22].…”