ABSTRACT
The fundamentals of output feedback H2 (linear quadratic Gaussian or LQG) and H∞ controllers, which are the primary synthesis tools available for linear time-invariant systems, are presented in an analogous and tutorial fashion without rigorous mathematics. Since H2 and H∞ syntheses are carried out in the modern control design paradigm, a review of the paradigm is presented, along with the definitions of the H2 and H∞ norms and the methods used to compute them. The state-space formulae for the optimal controllers, under less restrictive assumptions than are usually found in the literature, are provided in an analogous fashion to emphasize the similarities between them. Rather than emphasizing the derivation of the controllers, we elaborate on the physical interpretation of the results and how one uses frequency weights to design H∞ and H2 controllers. Finally, a simple disturbance rejection design for the longitudinal motion of an aircraft is provided to illustrate the similarities and differences between H∞ and H2 controller synthesis.
