Ebook: The Riccati Equation

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.

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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.

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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.
Content:
Front Matter....Pages I-X
Count Riccati and the Early Days of the Riccati Equation....Pages 1-10
Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review....Pages 11-51
Algebraic Riccati Equation: Hermitian and Definite Solutions....Pages 53-88
A Geometric View of the Matrix Riccati Equation....Pages 89-112
The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods....Pages 113-126
The Periodic Riccati Equation....Pages 127-162
Invariant Subspace Methods for the Numerical Solution of Riccati Equations....Pages 163-196
The Dissipation Inequality and the Algebraic Riccati Equation....Pages 197-242
The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints....Pages 243-262
Riccati Difference and Differential Equations: Convergence, Monotonicity and Stability....Pages 263-291
Generalized Riccati Equations in Dynamic Games....Pages 293-333
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.
Content:
Front Matter....Pages I-X
Count Riccati and the Early Days of the Riccati Equation....Pages 1-10
Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review....Pages 11-51
Algebraic Riccati Equation: Hermitian and Definite Solutions....Pages 53-88
A Geometric View of the Matrix Riccati Equation....Pages 89-112
The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods....Pages 113-126
The Periodic Riccati Equation....Pages 127-162
Invariant Subspace Methods for the Numerical Solution of Riccati Equations....Pages 163-196
The Dissipation Inequality and the Algebraic Riccati Equation....Pages 197-242
The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints....Pages 243-262
Riccati Difference and Differential Equations: Convergence, Monotonicity and Stability....Pages 263-291
Generalized Riccati Equations in Dynamic Games....Pages 293-333
Back Matter....Pages 335-338
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