Uncertain Models and Robust Control

I Introduction.- 1 Introductory Survey.- 2 Vector Norm. Matrix Norm. Matrix Measure.- 3 FUnctional Analysis, Function Norms and Control Signals.- II Differential Sensitivity. Small-Scale Perturbation.- 4 Kronecker Calculus in Control Theory.- 5 Analysis Using Matrices and Control Theory 79.- 6 Eigenvalue and Eigenvector Differential Sensitivity.- 7 Transition Matrix Differential Sensitivity.- 8 Characteristic Polynomial Differential Sensitivity.- 9 Optimal Control and Performance Sensitivity.- 10 Desensitizing Control.- III Robustness in the Time Domain.- 11 General Stability Bounds in Perturbed Systems.- 12 Robust Dynamic Interval Systems.- 13 Lyapunov-Based Methods for Perturbed Continuous-Time Systems.- 14 Lyapunov-Based Methods for Perturbed Discrete-Time Systems.- 15 Robust Pole Assignment.- 16 Models for Optimal and Interconnected Systems.- 17 Robust State Feedback Using Ellipsoid Sets.- 18 Robustness of Observers and Kalman-Bucy Filters.- 19 Initial Condition Perturbation, Overshoot and Robustness.- 20 Lpn-Stability and Robust Nonlinear Control.- IV Robustness in the Frequency Domain.- 21 Uncertain Polynomials. Interval Polynomials.- 22 Eigenvalues and Singular Values of Complex Matrices.- 23 Resolvent Matrix and Stability Radius.- 24 Robustness Via Singular-Value Analysis.- 25 Generalized Nyquist Stability of Perturbed Systems.- 26 Block-Structured Uncertainty and Structured Singular Value.- 27 Performance Robustness.- 28 Robust Controllers Via Spectral Radius Technique.- V Coprime Factorization and Minimax Frequency Optimization.- 29 Robustness Based on the Internal Model Principle.- 30 Parametrization and Factorization of Systems.- 31 Hardy Space Robust Design.- VI Robustness Via Approximative Models.- 32 Robust Hyperplane Design in Variable Structure Control.- 33 Singular Perturbations. Unmodelled High-Frequency Dynamics.- 34 Control Using Aggregation Models.- 35 Optimum Control of Approximate and Nonlinear Systems.- 36 System Analysis via Orthogonal Functions.- 37 System Analysis Via Pulse Functions and Piecewise Linear Functions.- 38 Orthogonal Decomposition Applications.- A Matrix Algebra and Control.- A.1 Matrix Multiplication.- A.2 Properties of Matrix Operations.- A.3 Diagonal Matrices.- A.4Triangular Matrices.- A.5 Column Matrices (Vectors) and Row Matrices.- A.6 Reduced Matrix, Minor, Cofactor, Adjoint.- A.7 Similar Matrices.- A.8 Some Properties of Determinants.- A.9 Singularity.- A.10 System of Linear Equations.- A.11 Stable Matrices.- A.12 Range Space. Rank. Null Space.- A.13 Trace.- A.14 Matrix Functions.- A.15 Metzler Matrices.- A.16 Projectors.- A.17 Projectors and Rank.- A.18 Projectors. Left-Inverse and Right-Inverse.- A.19 Trigonal Operator.- A.20 Transfer Function Zeros and Initial Step Transients.- A.21 Convolution Sum and TrigonalOperator.- B Eigenvalues and Eigenvectors.- B.1 Right-Eigenvectors.- B.2 Left-Eigenvectors.- B.3 Complex-Conjugate Eigenvalues.- B.4 Modal Matrix of Eigenvectors.- B.5 Complex Matrices.- B.6 Modal Decomposition.- B.7 Linear Differential Equations and Modal Transformations.- B.8 Eigenvalue Assignment.- B.9 Eigensystem Assignment.- B.10 Complete Modal Synthesis.- B.11 Vandermonde Matrix.- B.12 Decompostion into Eigenvectors.- B.13 Properties of Eigenvalues.- B.13.1 Smallest and Largest Eigenvalue of Symmetrie Matrices.- B.13.2 Eigenvalues and Trace.- B.13.3 Maximum Real Part of an Eigenvalue.- B.13.5 Adding the Identity Matrix.- B.13.6 Eigenvalues of Matrix Products.- B.13.7 Eigenvalue of a Matrix Polynomial.- B.13.8 Weyl Inequality.- B.14 Rayleigh’s Theorem.- B.15 Eigenvalues and Eigenvectors of the Inverse.- B.16 Dyadic Decomposition (Spectral Representation).- B.17 Spectral Representation of the Exponential Matrix.- B.18 Perron-Frobenius Theorem.- B.19 Multiple Eigenvalues. Generalized Eigenvectors.- B.20 Jordan Canonical Form and Jordan Blocks.- B.21 Special Cases.- B.22 Fundamental Matrix.- B.23 Eigenvector Assignment.- B.23.1 Assignable Subspaces. Parametrization ...