Robust Control of Linear Descriptor Systems - Practical Control Theory

In this review of Robust Control of Linear Descriptor Systems, the authors Yu Feng and Mohamed Yagoubi present a focused, theory-driven treatment that will appeal to control engineers and researchers who need methods beyond standard state-space models. The book's single biggest reason to buy is its systematic extension of classical control tools to the descriptor framework, offering both generalized LMI formulations and new viewpoints that help interpret controller architectures; this makes it particularly useful for those tackling singular or constrained dynamic systems. The review highlights clarity of purpose and originality rather than introductory pedagogy.

Key Features

• Generalization of classical results: The text translates familiar state-space results into the descriptor setting so readers can apply existing control intuition to singular systems.
• Dilated LMI characterizations: The book provides dilated linear matrix inequality formulations that help certify performance and stability for descriptor systems under practical constraints.
• Performance control under regulation constraints: It treats performance control problems explicitly, showing how regulation constraints are handled within the descriptor framework.
• Descriptor systems as a design tool: The authors demonstrate how viewing systems as descriptor models can lead to new control laws and unified derivations of known results.
• Comprehensive control problem example: The book uses a full control problem to illustrate how the descriptor approach can transform nonstandard problems into tractable designs.

Who It's For

This book is aimed at graduate students, academic researchers, and practicing control engineers who already have a grounding in state-space methods and linear matrix inequalities and who need to work with singular or constrained dynamic systems. It is particularly valuable for readers who want rigorous derivations that extend classical results into the descriptor domain.

Those seeking an introductory textbook on basic control concepts, an extensive set of worked numerical examples, or a practitioner manual with step-by-step implementation code should look elsewhere; the presentation is theoretical and assumes familiarity with advanced control mathematics and LMI techniques.

Pros & Cons

Pros

• Extends familiar state-space techniques into the descriptor framework, making it easier to transfer existing expertise.
• Provides dilated LMI characterizations that are useful for rigorous performance and stability analysis.
• Offers a novel perspective on controller architecture and unified derivations useful for researchers.

Cons

• The book is theoretical and concise, so readers wanting extensive numerical examples or implementation guidance may find it limited.

Specifications

Title	Robust Control of Linear Descriptor Systems
Series	Studies in Systems, Decision and Control, 102
Authors	Yu Feng, Mohamed Yagoubi
Focus	Descriptor systems, dilated LMI, performance control
Approach	Generalization of state-space results and new descriptor-based design paths
Audience	Graduate students, researchers, control engineers

Our Verdict

Robust Control of Linear Descriptor Systems is a concise, well-focused contribution that successfully extends classical control techniques to descriptor systems and introduces useful LMI-based tools; it is a good value for advanced students and researchers who need rigorous theory and unified derivations, but not for readers seeking hands-on tutorials or extensive implementation examples.

Frequently Asked Questions

Does this book require prior LMI knowledge?
Yes. The presentation assumes familiarity with linear matrix inequalities and advanced control theory.

Is it suitable for practical controller implementation?
It emphasizes theory and formulations rather than step-by-step implementation, so supplementary resources may be needed for coding controllers.

What unique perspective does it offer?
It treats descriptor systems as a design and unifying tool, offering new control laws and ways to homogenize state-space results.