We consider the problem of the perturbation of a class of linear-quadratic systems where the change from one structure (for the dynamics and costs) to another is governed by a finite-state Markov process. The problem above leads to the analysis of some perturbed linearly coupled set of Riccati equations. We show that the matrix obtained as the solution of the equations, which determines the optimal value and control, has a Taylor expansion in the perturbation parameter. We compute explicitly the terms of this expansion.