This paper addresses the analysis of switched linear systems using the invariant ellipsoid technique, numerically implemented through linear matrix inequalities. Two distinct cases are examined: arbitrary switching signals and switching signals bounded by dwell-time constraints. The search for invariant ellipsoids is formulated as semidefinite programming problems. For the arbitrary switching case, the solution employs a classical approach based on a common quadratic Lyapunov function. For the dwell-time constrained case, a system of linear matrix inequalities is derived using an established method that allows verifying the admissibility of a specified dwell-time. The solution to this system – a set of positive-definite matrices – is used to construct an invariant set as follows: an ellipsoid is associated with each matrix, and it is proven that any system trajectory starting within the intersection of these ellipsoids stays within their union. Numerical examples demonstrating the construction of invariant sets are provided for both cases.