  The propagation of a state vector is governed by a set of time-invariant
state transition matrices that switch arbitrarily between two values. The
evolution of the state is also perturbed by white Gaussian noise with a
variance that switches randomly with the state transition relation. The
behavior of this system can be characterized by the covariance matrix of the
state vector, which is time varying. However, we can bound the set of
covariances by comparing the switching system to an augmented system derived
with Kronecker algebra. We formulate a matrix optimization problem to compute
an ellipsoid that bounds the covariance dynamics, which in turn bounds the
state covariance of the set of switching systems subject to white noise. In
developing this approach, an invariant ellipsoid for a linear switching affine
system is computed along the way.
