Algorithm 2 Fault isolation with the minimal ${\ell }_1$-norm solution.
Input: $G\left(s\right)$, r(t)
1:	$G\leftarrow G\left(0\right)$
2:	$w\leftarrow \mathit{The\; number\; of\; data\; points\; to\; be\; averaged}$
3:	is_ fault ← False
4:	if $r_i\left(t\right)$ > threshold then
5:	is_ fault ← true
6:	if is_ fault & steady state then
7:	for $k<w$ do
8:	$r_m$ ← $r_m+r\left(k\right)$
9:	$r_m\leftarrow r_m/w$
10:	$e_1\left(0\right)\leftarrow G^{+}{r}_m$
11:	$e_1$ ← primal-dual algorithm($e_1\left(0\right),G,r_m$)
12:	return the number and locations of the nonzero components of $e_1$