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This is the second volume of a three-volume treatise which presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way. The work combines the features of a detailed introductory textbook with those of a reference source.

Volume II concentrates on problems of control, measurement and feedback control for time-varying and time-invariant linear systems. Special features are:

• a comprehensive treatment of controllability and observability
• an analysis of reachable sets under bounded controls with applications to the time-optimal control problem
• a detailed construction of canonical forms for controllable systems under similarity transformations, including an application of these forms to the topological analysis of system spaces
• a new module-theoretic approach to Rosenbrock systems in time domain
• an introduction to balancing and model reduction by balanced truncation
• an introduction to a general feedback control theory of input-output systems
• a detailed treatment of stabilization and observation problems for time-invariant linear systems
• a self-contained proof of Rosenbrock’s theorem by state space methods.

Throughout the book there are many examples, figures and exercises illustrating the text which help bring out the intuitive ideas behind the mathematical constructions. The book should be accessible to mathematics students after two years of study and also to engineering students with a good mathematical background. It will be of value for researchers in systems theory as well as for mathematicians and engineers who wish to learn about the mathematical foundations of the above topics.

More information on this book: https://link.springer.com/book/9783032083197

This is the third and final volume of Mathematical Systems Theory. Like the preceding volumes, it presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed, and mathematically rigorous manner. The exposition proceeds from the very general to the more specific, with rigorous mathematics complemented by numerous illustrations and explanatory remarks.

Volume III comprises two chapters and an appendix. In contrast to the first two volumes, only continuous-time systems are considered here. Chapter 9 addresses linear-quadratic optimal control and the Riccati equation, while Chapter 10 deals with zero dynamics and adaptive feedback regulation. Distinctive features include:

• a comprehensive treatment of the linear-quadratic optimal control problem
• a presentation of the bounded real and the Kalman–Yakubovich–Popov Lemma
• a systematic development of spectral factorization
• a study of the relative degree in state space and frequency domain
• a detailed exposition of the Byrnes–Isidori form and zero dynamics
• a development of the fundamentals of high-gain adaptive and funnel control.

The book combines the characteristics of a detailed introductory textbook with those of a reference source. The material should be accessible to mathematics students after two years of study, as well as to engineering students with a strong mathematical background. It will be of value to researchers in systems theory, as well as to mathematicians and engineers seeking to acquire a solid understanding of the mathematical foundations of the topics outlined above.

More information on this book: https://link.springer.com/book/9783032084002