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The Algebraic Riccati Equation for Quaternions
Advances in Applied Clifford Algebras, 2013The paper studies a Riccati equation \[ p(x):=a+bx+xc+xdx=0,\qquad a,b,c,d,x \in \mathbb{H}, \] where \(p\) is a quaternionic polynomial, which is shown to be reducible to a one-sided type. The set of quaternions \( \mathbb{H}\) can be seen as the four-dimensional vector space \( \mathbb{R}^4\) equipped with a special multiplication rule.
Janovská, Drahoslava, Opfer, Gerhard
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Algebraic Riccati equation and symplectic algebra
International Journal of Control, 1986Questions of existence, uniqueness and the parametric dependence of solutions of the algebraic Riccati equation are considered. The different criteria for the solubility of this equation are obtained with the help of symplectic algebra.
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The algebraic Riccati Equation (ARE)
Linear Systems Theory, 2018D. Bini, B. Meini, S. Bittanti
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In this paper, base on the theory of the non‐symmetric algebraic Riccati equation and the coupled Riccati equation, we give the general form of the non‐symmetric coupled algebraic Riccati equation (NCARE).
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Solving Time-Varying Nonsymmetric Algebraic Riccati Equations With Zeroing Neural Dynamics
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023The problem of solving algebraic Riccati equations (AREs) and certain linear matrix equations which arise from the ARE frequently occur in applied and pure mathematics, science, and engineering applications.
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