Matrix Riccati Equations in Control and Systems Theory

The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach.

The book is intended to make available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

• Control Theory
• Markov
• Operator
• Riccati Equations
• control engineering
• linear algebra
• systems theory
• ordinary differential equations

"In summary, this is a very well written and extremely useful book. It should be included in the library of everybody working on Ricatti equations, and in all areas of control, signals, and systems…. [It] will be a standard reference book in this area in the future."

—SIAM Review

• Ecole Normale Supérieure de Cachan, Laboratoire S.A.T.I.E. (UMR CNRS 8029), Cachan, France

  Hisham Abou-Kandil

• Institute of Mathematics, University of Duisburg, Duisburg, Germany

  Gerhard Freiling

• Department of Mathematics, University of Bucharest, Romania

  Vlad Ionescu

• Institut für Mathematik, RWTH Aachen, Aachen

  Gerhard Jank

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