Takao Nambu
Theory of Stabilization for Linear Boundary Control Systems
Theory of Stabilization for Linear Boundary Control Systems
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- More about Theory of Stabilization for Linear Boundary Control Systems
The book presents a unified algebraic approach to stabilization problems of linear boundary control systems, providing a new proof of the stabilization result for finite-dimensional systems and discussing output stabilization when observability or controllability conditions are not satisfied.
Format: Paperback / softback
Length: 284 pages
Publication date: 31 March 2021
Publisher: Taylor & Francis Ltd
This book offers a comprehensive algebraic framework for addressing stabilization issues in linear boundary control systems, without imposing any assumptions on finite-dimensional approximations of the original systems. It introduces a novel proof of the stabilization theorem for linear systems of finite dimension, resulting in a precise design of the feedback scheme. The book also explores the problem of output stabilization and presents valuable insights when the observability or controllability conditions are not met.
Book Title: "Stabilization of Linear Boundary Control Systems"
This book presents a unified algebraic approach to stabilization problems of linear boundary control systems, providing a comprehensive framework for analyzing and designing feedback control schemes. It emphasizes the absence of assumptions on finite-dimensional approximations to the original systems, allowing for a more general and flexible treatment of the stabilization problem. The book introduces a new proof of the stabilization theorem for linear systems of finite dimension, leading to an explicit design of the feedback scheme. Additionally, the book discusses the problem of output stabilization and presents interesting results when the observability or controllability conditions are not satisfied. The book is suitable for researchers and graduate students in the fields of control theory and applied mathematics.
Introduction
Linear boundary control systems are a fundamental class of control systems that play a crucial role in various applications, including robotics, aerospace, and industrial process control. These systems consist of a linear plant, a boundary control law, and a feedback controller. The goal of stabilization is to ensure that the closed-loop system is stable and satisfies certain performance criteria, such as boundedness of the state and output signals. However, the stabilization of linear boundary control systems is a challenging task due to the presence of nonlinearities, uncertainties, and constraints. Traditional control theory approaches often rely on finite-dimensional approximations of the original systems, which can lead to inaccurate results and limited applicability. In this book, we present a unified algebraic approach to stabilization that does not require any assumptions on finite-dimensional approximations. This approach allows us to develop a more general and flexible framework for analyzing and designing feedback control schemes.
Unified Algebraic Approach
The unified algebraic approach to stabilization of linear boundary control systems is based on the concept of the Riesz basis. A Riesz basis is a set of vectors in a Hilbert space that is complete and orthonormal, and it provides a basis for the space of all square-integrable functions. The Riesz basis can be used to represent the state and output signals of the linear boundary control system. The stabilization problem is then formulated as a problem of finding a feedback controller that stabilizes the system while minimizing a certain performance criterion. The unified algebraic approach allows us to develop a systematic and efficient method for solving this problem. It involves the use of matrix algebra, linear programming, and optimization techniques. The book presents a new proof of the stabilization theorem for linear systems of finite dimension, leading to an explicit design of the feedback scheme. The proof is based on the concept of the Riesz basis and the properties of the associated operator. The proof is concise and easy to understand, and it provides a solid foundation for the development of feedback control schemes. The book also discusses the problem of output stabilization and presents interesting results when the observability or controllability conditions are not satisfied. The book is suitable for researchers and graduate students in the fields of control theory and applied mathematics.
New Proof of the Stabilization Theorem
The stabilization theorem for linear systems of finite dimension is a fundamental result in control theory. It states that a linear system with a finite-dimensional state space can be stabilized by a feedback controller that is designed using the Riesz basis. The proof of the stabilization theorem is usually based on the Lyapunov stability theory. However, the Lyapunov stability theory can be complex and difficult to apply in practice. In this book, we present a new proof of the stabilization theorem that is based on the concept of the Riesz basis. The proof is concise and easy to understand, and it provides a solid foundation for the development of feedback control schemes. The proof is based on the concept of the Riesz basis and the properties of the associated operator. The proof is concise and easy to understand, and it provides a solid foundation for the development of feedback control schemes. The book also discusses the problem of output stabilization and presents interesting results when the observability or controllability conditions are not satisfied. The book is suitable for researchers and graduate students in the fields of control theory and applied mathematics.
Output Stabilization
Output stabilization is a crucial aspect of linear boundary control systems. It involves the design of a feedback controller that ensures that the output signals of the system are bounded and stable. The problem of output stabilization is challenging due to the presence of nonlinearities, uncertainties, and constraints. Traditional control theory approaches often rely on finite-dimensional approximations of the original systems, which can lead to inaccurate results and limited applicability. In this book, we discuss the problem of output stabilization and present interesting results when the observability or controllability conditions are not satisfied. The book presents a new proof of the stabilization theorem for linear systems of finite dimension, leading to an explicit design of the feedback scheme. The proof is based on the concept of the Riesz basis and the properties of the associated operator. The proof is concise and easy to understand, and it provides a solid foundation for the development of feedback control schemes. The book also discusses the problem of output stabilization and presents interesting results when the observability or controllability conditions are not satisfied. The book is suitable for researchers and graduate students in the fields of control theory and applied mathematics.
Conclusion
In conclusion, this book presents a unified algebraic approach to stabilization problems of linear boundary control systems, providing a comprehensive framework for analyzing and designing feedback control schemes. It emphasizes the absence of assumptions on finite-dimensional approximations to the original systems, allowing for a more general and flexible treatment of the stabilization problem. The book introduces a new proof of the stabilization theorem for linear systems of finite dimension, leading to an explicit design of the feedback scheme. Additionally, the book discusses the problem of output stabilization and presents interesting results when the observability or controllability conditions are not satisfied. The book is suitable for researchers and graduate students in the fields of control theory and applied mathematics.
Weight: 526g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367782818
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