LQ feedback formulation for H-infinity output feedback control

In this thesis we present a simple, unified formula for discrete and continuous-time Hinfinity "all-solutions" controllers. By observing a "cost" equivalence between the standard Hinfinity control problem and a certain LQ optimal regulator problem, an elegant controller structure reminiscent of an LQG optimal controller is developed. Our choice of notation also simplifies the derivation and existence conditions considerably, whereby all unnecessary assumptions on plant state-space matrices and "loop-shifting" transformations are eliminated. Additionally, with our focus entirely on input-output weighting "cost functions" this derivation offers a "behavioral" theory interpretation for all solutions of a standard H infinity control problem.;In this thesis we also present a simplified matrix pencil formula for solving the Hinfinity control problem for the case 0 ≤ sigmamax(D11) ≤ gamma. This formula is useful in developing a more numerically robust algorithm in Hinfinity control. A significant feature of this formula is that each element of the pencils is expressed directly in terms of the original descriptor-form state space matrices of the plant and even pencil eigenspaces computed using a numerically robust even pencil algorithm. There are no data-corrupting numerical operations required to form any of the matrices that appear in our "all-solutions" controller formula.