MATHGALLERY

The cheap control regulator for time-invariant systems is studied with respect to uniform -boundedness of the state trajectories in the case where the small parameter "" tends to zero. By using the geometric approach, state-space conditions for -boundedness are found and related to the concept of zero dynamics... In this thesis we study the cheap control regulator in the limiting case where the small parameter "" tends to zero. Francis and Glover [1] have given conditions in the frequency domain for uniform -boundedness of the state trajectories in this case... However, restating these conditions in the time domain (state-space) gives a more intuitive picture of the dynamic behavior of the closed-loop system and is essential for the generalization of these conditions to nonlinear systems.