Linear System Theory and Design 3rd Edition by Chi Tsong Chen 0195117778 978-0195117776

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ISBN 10: 0195117778

ISBN 13: 978-0195117776

Author: Chi-Tsong Chen

Linear System Theory and Design 3rd Table of contents:

Chapter 1: Introduction

1.1 Introduction

Foundational concepts and context for the subject matter.

1.2 Overview

Summary of the chapter’s content and its significance.

Chapter 2: Mathematical Descriptions of Systems

2.1 Introduction

Basics of system modeling and mathematical frameworks.

2.1.1 Causality and Lumpedness

Discussion on causality and lumped parameter systems.

2.2 Linear Systems

Principles and characteristics of linear systems.

2.3 Linear Time-Invariant (LTI) Systems

Detailed analysis of LTI systems.

2.3.1 Op-Amp Circuit Implementation

Application of LTI concepts in operational amplifier circuits.

2.4 Linearization

Methods for linearizing nonlinear systems.

2.5 Examples

Practical examples illustrating theoretical concepts.

2.5.1 RLC Networks

Modeling and analysis of RLC circuits.

2.6 Discrete-Time Systems

Examination of systems operating in discrete time.

2.7 Concluding Remarks

Key takeaways and summary of the chapter.

Problems

Exercises to reinforce understanding.

Chapter 3: Linear Algebra

3.1 Introduction

Overview of linear algebra’s role in system analysis.

3.2 Basis, Representation, and Orthonormalization

Basics of vector spaces, orthonormalization, and basis representation.

3.3 Linear Algebraic Equations

Techniques for solving linear systems of equations.

3.4 Similarity Transformation

Simplifying matrix analysis via similarity transformations.

3.5 Diagonal Form and Jordan Form

Decomposing matrices for easier computation.

3.6 Functions of a Square Matrix

Utilizing functions to analyze square matrices.

3.7 Lyapunov Equation

Solutions to the Lyapunov equation in stability analysis.

3.8 Some Useful Formulas

Key mathematical tools and their applications.

3.9 Quadratic Form and Positive Definiteness

Analyzing quadratic forms and positive definite matrices.

3.10 Singular-Value Decomposition

Understanding singular-value decomposition and its uses.

3.11 Norms of Matrices

Definitions and applications of matrix norms.

Problems

Practice exercises for skill enhancement.

Chapter 4: State-Space Solutions and Realizations

4.1 Introduction

Overview of state-space representations and realizations.

4.2 Solution of LTI State Equations

Methods for solving state-space equations in LTI systems.

4.2.1 Discretization

Techniques for transitioning to discrete-time systems.

4.2.2 Solution of Discrete-Time Equations

Solving equations for discrete-time models.

4.3 Equivalent State Equations

Analysis of state equations with equivalent representations.

4.3.1 Canonical Forms

Representation of state equations in canonical form.

4.3.2 Magnitude Scaling in Op-Amp Circuits

Scaling techniques for operational amplifiers.

4.4 Realizations

Practical realizations of state-space models.

4.5 Solution of Linear Time-Varying (LTV) Equations

Solving equations for systems with time-variant characteristics.

4.5.1 Discrete-Time Case

Special considerations for discrete-time systems.

4.6 Equivalent Time-Varying Equations

Deriving equivalent forms for time-varying systems.

4.7 Time-Varying Realizations

Implementing realizations for time-varying systems.

Problems

Exercises to deepen understanding.

Chapter 5: Stability

5.1 Introduction

Key concepts in system stability.

5.2 Input-Output Stability of LTI Systems

Analyzing stability in input-output relationships.

5.2.1 Discrete-Time Case

Addressing stability in discrete-time systems.

5.3 Internal Stability

Discussion on internal system stability.

5.3.1 Discrete-Time Case

Discrete-time considerations for internal stability.

5.4 Lyapunov Theorem

Application of the Lyapunov theorem in stability analysis.

5.4.1 Discrete-Time Case

Lyapunov stability for discrete systems.

5.5 Stability of LTV Systems

Stability considerations for time-varying systems.

Problems

Practice problems for stability analysis.

Chapter 6: Controllability and Observability

6.1 Introduction

Overview of system controllability and observability.

6.2 Controllability

Analyzing the controllability of dynamic systems.

6.2.1 Controllability Indices

Metrics for assessing controllability.

6.3 Observability

Exploring the observability of systems.

6.3.1 Observability Indices

Metrics for measuring observability.

6.4 Canonical Decomposition

Decomposing systems into canonical forms.

6.5 Conditions in Jordan-Form Equations

Constraints in Jordan-form representations.

6.6 Discrete-Time State Equations

Special considerations for discrete-time models.

6.6.1 Controllability to the Origin and Reachability

Specific scenarios in discrete-time controllability.

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