Perturbation of multivariable linear quadratic systems with jump parameters

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 le ads to the analysis of some perturbed linearly coupled set of Riccati equat ions. We show that the matrix obtained as the solution of the equations, wh ich determines the optimal value and control, has a Taylor expansion in the perturbation parameter. We compute explicitly the terms of this expansion.