The H∞ 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.