Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory. The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory.

This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor systems, such as dilated linear matrix inequality (LMI) characterizations for descriptor systems and performance control under regulation constraints. The second is a new path, which considers descriptor systems as a powerful tool for conceiving new control laws, understanding and deciphering some controller’s architecture and even homogenizing different—existing—ways of obtaining some new and/or known results for state-space systems. The book also highlights the comprehensive control problem for descriptor systems as an example of using the descriptor framework in order to transform a non-standard control problem into a classic stabilization control problem. In another section, an accurate solution is derived for the sensitivity constrained linear optimal control also using the descriptor framework. The book is intended for graduate and postgraduate students, as well as researchers in the field of systems and control theory.

The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation.

Although LMI has emerged as a powerful tool with applications across the major domains of systems and control, there has been a need for a textbook that provides an accessible introduction to LMIs in control systems analysis and design. Filling this need, LMIs in Control Systems: Analysis, Design and Applications focuses on the basic analysis and d

Provides One Unified Formula That Gives Solutions to Several Types of GSEsGeneralized Sylvester equations (GSEs) are applied in many fields, including applied mathematics, systems and control, and signal processing. Generalized Sylvester Equations: Unified Parametric Solutions presents a unified parametric approach for solving various types of GSEs

This book shows how the use of S-variables (SVs) in enhancing the range of problems that can be addressed with the already-versatile linear matrix inequality (LMI) approach to control can, in many cases, be put on a more unified, methodical footing. Beginning with the fundamentals of the SV approach, the text shows how the basic idea can be used for each problem (and when it should not be employed at all). The specific adaptations of the method necessitated by each problem are also detailed. The problems dealt with in the book have the common traits that: analytic closed-form solutions are not available; and LMIs can be applied to produce numerical solutions with a certain amount of conservatism. Typical examples are robustness analysis of linear systems affected by parametric uncertainties and the synthesis of a linear controller satisfying multiple, often conflicting, design specifications. For problems in which LMI methods produce conservative results, the SV approach is shown to achieve greater accuracy. The authors emphasize the simplicity and easy comprehensibility of the SV approach and show how it can be implemented in programs without difficulty so that its power becomes readily apparent. The S-variable Approach to LMI-based Robust Control is a useful reference for academic control researchers, applied mathematicians and graduate students interested in LMI methods and convex optimization and will also be of considerable assistance to practising control engineers faced with problems of conservatism in their systems and controllers.

Control of Linear Parameter Varying Systems compiles state-of-the-art contributions on novel analytical and computational methods for addressing system identification, model reduction, performance analysis and feedback control design and addresses address theoretical developments, novel computational approaches and illustrative applications to various fields. Part I discusses modeling and system identification of linear parameter varying systems, Part II covers the importance of analysis and control design when working with linear parameter varying systems (LPVS) , Finally, Part III presents an applications based approach to linear parameter varying systems, including modeling of a turbocharged diesel engines, Multivariable control of wind turbines, modeling and control of aircraft engines, control of an autonomous underwater vehicles and analysis and synthesis of re-entry vehicles.