Some remarks on FSN models and generalized Riccati equations

In the framework of FSN models, the covariance of the noise corrupting a signal is taken to be linearly related to the variance of that signal. If compared to the standard assumptions typical of LQG control/estimation theory. this allows for a more realistic modeling and leads to robust solutions of the control/estimation problems. Here we consider the particular case where only the control signal is seen as an extra source of noise and consider an optimal control problem with finite horizon and quadratic performance index. Connections with previous results are presented, together with some remarks on stability issues.