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Contents 1 Robust feedback Conti 1. 1 Feedback and Uncertainty 1. 2 Classical Com pensator De sign Metho ds 1. 3 Mo del Uncertainty. 1. 4 Feedback Systems with Model Uncertainties 1.5 Robust Control Nominal and Robust Stability 1357799 2.1 A Model of the proces 2.2 Mo del Uncertainty 2.3 Nominal Stability 2.4 Robust Stability. 3 Nominal and robust performance 13 3.1 Signal No 3.2 Norms for Systems and Transfer Functions 3.3 Specification of inputs 3.4 Requirements for Perform ance 3.5 H2 Optimal Control(LQ) 3.6H。 Optim al 3.7 Robust Perform an ce 3.8 H2 Robust Performance 3.9 Hoo Robust P n ce 3.10 Loop Shaping 4 An Introduction to Multivariable Systems 26 4.1 Poles and zeros of multi ariable Sy stems 4.1.1 Smith-McMillan Form of a Transfer matrix 4.2 Nominal Stability for Multivariable Systems 4.2.1 Internal Stability 4.2.2 The Generalized Ny quist Theorem 4.3 Frequency Responses for Multiv ariable Systems 3 4.3. 2 Induced Norms 4.3.3 Singular values ! " # $ % % & ! & & # ' # ! ( # ! )! # $ # * + ,-./ % 0 + % ! $ # 1 * ! $ # % ! $ # 1 - $ 2 # ! 3 0 4 # ' # 5 1 & # ! 3 6 ' 7 2 &)! ' )! # ! 3 8 & * 6 ! & * ! 8! *