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Perturbation Theory for Discrete Algebraic Riccati Equations
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Abstract
Taking advantage of the geometric theory for the discrete algebraic Riccati equation developed in Chapter 12, as well as the comparison theorems of Chapter 13, we can now study the behaviour of hermitian solutions of discrete algebraic Riccati equations under small perturbations of the coefficients of these equations. The emphasis is on the behaviour of extremal (minimal and maximal) solutions. Their behaviour as functions of the coefficients is studied here as well. The material of this chapter is, of course, the analogue of that in Chapter 11 and is developed here for the DARE of equation (12.2.1) rather than the CARE of equation (7.2.1).
Title: Perturbation Theory for Discrete Algebraic Riccati Equations
Description:
Abstract
Taking advantage of the geometric theory for the discrete algebraic Riccati equation developed in Chapter 12, as well as the comparison theorems of Chapter 13, we can now study the behaviour of hermitian solutions of discrete algebraic Riccati equations under small perturbations of the coefficients of these equations.
The emphasis is on the behaviour of extremal (minimal and maximal) solutions.
Their behaviour as functions of the coefficients is studied here as well.
The material of this chapter is, of course, the analogue of that in Chapter 11 and is developed here for the DARE of equation (12.
2.
1) rather than the CARE of equation (7.
2.
1).
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