  In this work, we obtain sufficient conditions for the ``stability" of our
recently proposed algorithms, modified-CS (for noisy measurements) and Least
Squares CS-residual (LS-CS), designed for recursive reconstruction of sparse
signal sequences from noisy measurements. By ``stability" we mean that the
number of misses from the current support estimate and the number of extras in
it remain bounded by a time-invariant value at all times. The concept is
meaningful only if the bound is small compared to the current signal support
size. A direct corollary is that the reconstruction errors are also bounded by
a time-invariant and small value.
