The H {Infinity} Control Problem

Part 1 Introduction: robustness analysis; the infinity control problem; stabilization of uncertain systems; the graph topology; the mixed-sensitivity problem; main items of this book - singular systems, differential game, the minimum entropy infinity control problem, the finite horizon infinity control problem, discrete time systems. Part 2 Notation and basic properties: introduction; linear systems - continuous time, discrete time; rational matrices; geometric theory; the Hardy and Lebesgues spaces - continuous time, discrete time; (almost) disturbance decoupling problems. Part 3 The regular full-information infinity control problem: introduction; problem formulation and main results; intuition for the formal proof; solvability of the Riccati equation; existence of a suitable controller. Part 4 The general full-information infinity control problem: introduction; problem formulation and main results; solvability of the quadratic matrix inequality; existence of state feedback laws; the design of a suitable compensator; a direct feed through matrix from disturbance to output; invariant zeros on the imaginary axis - frequency domain loop shifting, cheap control; conclusion. Part 5 The infinity control problem with measurement feedback: introduction; problem formulation and main results; reduction of the original problem to an almost disturbance decoupling problem; the design of a suitable compensator; characterization of achievable closed loop systems; no assumptions on any direct feedthrough matrix - an extra direct-feedthrough matrix from disturbance to output, an extra direct-feedthrough matrix from control to measurement; conclusion. Part 6 The singular zero-sum differential game with stability: introduction; problem formulation and main results; existence of almost equilibria; necessary conditions for the existence of almost equilibria; the regular differential game; conclusions. Part 7 The singular minimum entropy infinity control problem: introduction; problem formulation and results; properties of the entropy function; a system transformation; (almost) disturbance decoupling and minimum entropy; conclusion. Part 8 The finite horizon finite control problem: introduction; problem formualtion and main results; completion of the squares; existence of compensators; concluding remarks.