Contents Preface Notation and Symbols List of acronyms XvII 1 Introduction 1.1 What Is This book about? 1.2 Highlights of This Book 3 1. 3 Notes and references 9 2 Linear Algebra 2.1 Linear Subspaces 2.2 Eigenvalues and eigenvectors 2.3 Matrix Inversion Formulas 2.4 Invariant Subspaces 2.5 Vector Norms and Matrix Norms 6 Singular Value Decomposition 2.7 Semidefinite Matrices 2. 8 Notes and References 2.9 Problems 3 Linear Systems 3.1 Descriptions of Linear Dynamical Systems 3.2 Controllability and Observability 3.3 Observers and Observer-Based Controllers 31 3.5 State-Space Realizations for Transfer Matrices 3.6 Multivariable System Poles and Zeros 3.7 Notes and ReferencesContents Preface vii Notation and Symbols xv List of Acronyms xvii 1 Introduction 1 1.1 What Is This Book About? ......................... 1 1.2 Highlights of This Book ........................... 3 1.3 Notes and References ............................. 9 1.4 Problems ................................... 10 2 Linear Algebra 11 2.1 Linear Subspaces ............................... 11 2.2 Eigenvalues and Eigenvectors ........................ 12 2.3 Matrix Inversion Formulas .......................... 13 2.4 Invariant Subspaces ............................. 15 2.5 Vector Norms and Matrix Norms ...................... 16 2.6 Singular Value Decomposition ........................ 19 2.7 Semidefinite Matrices ............................ 23 2.8 Notes and References ............................. 24 2.9 Problems ................................... 24 3 Linear Systems 27 3.1 Descriptions of Linear Dynamical Systems ................. 27 3.2 Controllability and Observability ...................... 28 3.3 Observers and Observer-Based Controllers ................. 31 3.4 Operations on Systems ............................ 34 3.5 State-Space Realizations for Transfer Matrices .............. 35 3.6 Multivariable System Poles and Zeros ................... 38 3.7 Notes and References ............................. 41 3.8 Problems ................................... 42 xi