Cover -- Title -- Copyright -- Foreword -- Preface -- Table of Contents -- 1 Introduction -- 1.1 Some Biased Historical Notes -- 1.2 Scope and Organization -- 2 Mathematical Background: Matrix Analysis and Computation -- 2.1 Introduction and Basic Notions -- Simultaneous Linear Algebraic Equations -- Numerical Methods to Solve the Least Square Problem -- Partitioned Matrix Inversion Formulas and the Matrix Inversion Lemma -- 2.2 Matrix Decompositions -- Spectral Decomposition -- Singular Value Decomposition -- Cholesky Decomposition
Schur Decomposition2.3 Sensitivity and Conditioning Issues -- Eigenvalue/Eigenvector Sensitivities -- Conditioning of Eigenvalue Problem -- Stability Robustness Criteria: Conditioning of the Eigenstructure -- Partial Derivatives of the Singular Values -- 2.4 Case Study: Parameterization of Orthogonal Matrices -- Some Geometrical and Kinematical Insignts from R[sup(3Ã?3)] -- Parameterizations of Orthogonal Matrices in R[sup(nÃ?n)] -- Applications of the Cayley Transform -- 3 Stability in the Sense of Lyapunov: Theory and Applications -- 3.1 Basic Definitions
3.2 Lyapunov's Stability Theorem (Direct Method)3.3 Stability of Linear Systems -- Lyapunov Theorem for Linear Systems -- Linear Dynamic Systems Subject to Arbitrary Disturbances -- Stability Analysis for Mechanical Second Order Systems -- 3.4 Nonlinear, Time Varying, and Distributed Parameter Systems -- Local Stability of Linearized Systems -- What to do When U is Only Negative Semi-Definite -- Lyapunov Control Law Design Method -- Work Energy Rate Principle and Laypunov Stable Control Laws -- Globally Stable Tracking Controller: Lyapunov Approach
3.5 Case Study: Application for Near-Minimum-Time Large Angle Maneuvers of Distributed Parameter SystemsSimulated Results for the Large Angle Maneuvers -- Experimental Results -- 4 Mathematical Models of Flexible Structures -- 4.1 Lagrangian Approach to Equation of Motion Formulation -- 4.2 Infinite-Dimensional Models of Distributed Parameter Systems -- Classical Application of Hamilton's Principle -- Explicit Generalization of Lagrange's Equations -- The Differential Eigenvalue Problem -- 4.3 Approximate Methods for Finite Dimensional Models -- Assumed Modes Method
Finite Element MethodComparison Between Two Spatial Discretization Models -- 4.4 Case Study: Consequences of Neglecting Coupling between Rigid Motion and Elastic Motion -- 5 Design of Linear State Feedback Control Systems -- 5.1 Linear Optimal Control -- Necessary Conditions for Optimality -- Linear Regulator Problem -- Numerical Algorithms for Solving the Riccati Equations -- Generalized Linear Quadratic Regulator Formulations -- 5.2 Robust Eigenstructure Assignment -- Sylvester's Equation -- Projection Method for Eigenstructure Assignment
