The Riccati Equation

1. Front Matter

   Pages I-X

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2. Count Riccati and the Early Days of the Riccati Equation

   • Sergio Bittanti

   Pages 1-10

3. Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review

   • Peter Lancaster, Leiba Rodman

   Pages 11-51

4. Algebraic Riccati Equation: Hermitian and Definite Solutions

   • Vladimír Kučera

   Pages 53-88

5. A Geometric View of the Matrix Riccati Equation

   • Mark A. Shayman

   Pages 89-112

6. The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods

   • Clyde F. Martin, Gregory Ammar

   Pages 113-126

7. The Periodic Riccati Equation

   • Sergio Bittanti, Patrizio Colaneri, Giuseppe De Nicolao

   Pages 127-162

8. Invariant Subspace Methods for the Numerical Solution of Riccati Equations

   • Alan J. Laub

   Pages 163-196

9. The Dissipation Inequality and the Algebraic Riccati Equation

   • H. L. Trentelman, Jan C. Willems

   Pages 197-242

10. The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints

    • Jacques L. Willems, Frank M. Callier

    Pages 243-262

11. Riccati Difference and Differential Equations: Convergence, Monotonicity and Stability

    • Robert R. Bitmead, Michel Gevers

    Pages 263-291

12. Generalized Riccati Equations in Dynamic Games

    • Tamer Başar

    Pages 293-333

13. Back Matter

    Pages 335-338

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Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

• Algebra
• algorithm
• algorithms
• control
• control theory
• geometry
• history
• network
• optimal control
• optimization
• quality
• stability
• stabilization
• system theory
• systems theory

• Dipartimento di Elettronica, Politecnico di Milano, Milano, Italy

  Sergio Bittanti

• Department of Electrical and Computer Engineering, University of California, Santa Barbara, USA

  Alan J. Laub

• Department of Mathematics, University of Groningen, Groningen, The Netherlands

  Jan C. Willems

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