Contents Ffe Notation and Symbols xiii List o.Acronyms 1 Introductipp 1 1.1 What his 1 1.2 Highlights his ook 3 1.3 Lotes and 9 8 Lin Alg ra 11 2.1 11 2.2 Ligenvalues and e nvectors 12 2.3 Mat rix version Brmuas· 13 2.4 ←bspaces ，。。。。。。。。。。。 14 2.5 ector ms and Matrix 6 ngular Value Decomposition. 18 2 emidefinits Matrices 3 . Lotes and leferences. 2.9 Problems 24 Linr Syst(品s 89 3.1 scriptions of Dy namical 。。 ntrollability 2 rvers and rver- ontrollers stems.·· izations for ansfer Matrices 3 6 stem Poles and Zeros Lotes and eferences·· 。。。。。。。。 4 3.8 Problems 42 viiContents Preface v Notation and Symbols xiii List of Acronyms xv Introduction  What This Book Is About ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Highlights of This Book ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Notes and References ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾  Linear Algebra  Linear Subspaces ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Eigenvalues and Eigenvectors ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Matrix Inversion Formulas ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Invariant Subspaces ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Vector Norms and Matrix Norms ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Singular Value Decomposition ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Semidenite Matrices ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Notes and References ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Problems ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Linear Systems   Descriptions of Linear Dynamical Systems ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Controllability and Observability ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Observers and ObserverBased Controllers ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Operations on Systems ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   State Space Realizations for Transfer Matrices ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Multivariable System Poles and Zeros ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Notes and References ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾   Problems ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾ ￾  vii