Numerical Methods for Linear Control Systems (Hardcover)

Description:

Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. MATLAB-based software is included for implementing all of the major algorithms from the book.

 

Table of Contents:

Introduction and Overview; Review of Basic Concepts and Results from Theoretical Linear Algebra; Fundamental Tools and Concepts from Numerical Linear Algebra; Canonical Forms Obtained via Orthogonal Transformations; Linear State Space Models and Solutions of the State Equations; Contollability, Observability and Distance to Uncontrollability; Stability, Inertia and Robust Stability; Numerical Solutions and Conditioning of Lyapunov and Sylvester Equations; Realization and Subspace Identification; Feedback Stabilization, Eigenvalue Assignment and Optimal Control; Numerical Methods and Conditioning of the Eigenvalue Assignment Problems; State Estimation; Numerical Solutions and Conditioning of Algebraic Riccati Equations; Internal Balancing and Model Reduction; Large-Scale Matrix Computations in Control: Krylov Subspace Methods; Numerical Methods for Matrix-Second-Order Control Systems; Existing Software for Control Systems Design and Analysis

 

描述：
《線性控制系統設計和分析的數值方法》是一本跨學科教材，旨在系統地描述和實現基於確立、高效和穩定的現代數值線性技術的可行算法，用於設計和分析線性控制系統的數學問題，包括一階和二階模型。書中包含了基於MATLAB的軟件，用於實現書中的所有主要算法。

目錄：
引言和概述；從理論線性代數中回顧基本概念和結果；從數值線性代數中獲得的基本工具和概念；通過正交變換獲得的規範形式；線性狀態空間模型和狀態方程的解；可控性、可觀性和不可控性距離；穩定性、慣性和魯棒穩定性；Lyapunov和Sylvester方程的數值解和條件；實現和子空間識別；反饋穩定化、特徵值分配和最優控制；特徵值分配問題的數值方法和條件；狀態估計；代數Riccati方程的數值解和條件；內部平衡和模型簡化；控制中的大規模矩陣計算：Krylov子空間方法；矩陣二階控制系統的數值方法；用於控制系統設計和分析的現有軟件。