15. Optimal Control in MIMO Systems

In this chapter, we utilize the norms discussed in the previous chapter to derive MIMO controllers. As the discussion of ℋ₂ and ℋ_∞ MIMO control design are topics of robust optimal control domain, it would be beneficial to start with having a brief discussion on LQG (Linear Quadratic Gaussian) control, which is a well-established MIMO technique. Our intent is to discuss what the main drawbacks of LQG method were and how the techniques such as ℋ_∞ control method address these drawbacks. It should be noted that all the optimal controllers are derived based on the linearity and infinite horizon assumptions, as t → ∞.