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Generalized Riccati theory and robust control. A Popov function approach. (English) Zbl 0915.34024
Chichester: John Wiley & Sons. xii, 380 p. (1999).
This book is a comprehensive presentation of the approach proposed by Popov to the theory of algebraic Riccati equations and its applications to the robust control of linear dynamical systems. Riccati equations provide a convenient framework, together with sound and stable numerical algorithms. The book encompasses many results in control systems theory that are related to Riccati equations.
Part I introduces and outlines some background results in linear algebra. In Part II the basic setting for Popov’s approach to the Riccati equation theory is introduced. The central notion here is the Popov triplet. Chapters 4, 5 and 6 present the core of the authors’ approach as they contain main existence results for the stabilizing solution. Chapter 5 is primarily concerned with computational aspects of the theory. Finally, Part III includes five chapters which comprise mathematical problems of system theory and robust control.
The book is the first monograph to give a systematic account on algebraic Riccati equations with an indefinite sign quadratic term.

34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
15A22 Matrix pencils
47N70 Applications of operator theory in systems, signals, circuits, and control theory
93B36 \(H^\infty\)-control
93D10 Popov-type stability of feedback systems
93D21 Adaptive or robust stabilization
34H05 Control problems involving ordinary differential equations