  Efficient computation of trajectories of switched affine systems becomes
possible, if for any such hybrid system, we can manage to efficiently compute
the sequence of switching times. Once the switching times have been computed,
we can easily compute the trajectories between two successive switches as the
solution of an affine ODE. Each switching time can be seen as a positive real
root of an analytic function, thereby allowing for efficient computation by
using root finding algorithms. These algorithms require a finite interval,
within which to search for the switching time. In this paper, we study the
problem of computing upper bounds on such switching times, and we restrict our
attention to stable time-invariant affine systems. We provide semi-definite
programming models to compute upper bounds on the time taken by the
trajectories of an affine ODE to exit a set described as the intersection of a
few generalized ellipsoids. Through numerical experiments, we show that the
resulting bounds are tighter than bounds reported before, while requiring only
a modest increase in computation time.
