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"Fractional Tuning" of the Riccati Equation
Fractals, 1997The dynamics of a free-falling body in complex materials such as a polymer fluid is phenomenologically modeled using a fractional generalization of the Riccati equation. The solution exhibits a rich behavior in its parametric dependence, and unlike normal free–fall there is no terminal velocity, instead a power–law increase in time is obtained. Within
Metzler, R. +3 more
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Controllability Conditions for the Riccati Equation
Differential Equations, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Riccati Matrix Differential Equations
Results in Mathematics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knobloch, H. W., Pohl, M.
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Generalized Operator Riccati Equations
SIAM Journal on Mathematical Analysis, 1985Summary: The Riccati equation \(dU/dt=AU+UB^*+UCU+D\) on the space \({\mathcal L}(X)\) of bounded linear operators on a reflexive Banach space X arises in control theory and transport theory. A more general problem is the following. Let A and B be closed linear operators in X and \(X^*\) respectively and let \({\mathcal F}\) be a map from [0,T)\(\times
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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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Matrix Riccati Differential Equations
Journal of the Society for Industrial and Applied Mathematics, 1965Chiellini [1] considered this system, and showed that knowledge of n solutions, not on the same (n 2) -flat, reduced the solution to quadratures (this generalizes (I)). In [2] it was shown that knowledge of k suitably independent solutions, 1 < k < n, reduces the solution to k quadratures and the solution of a matrix-vector linear homogeneous system of
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Mixed Riccati equations and contractiveness
1999 European Control Conference (ECC), 1999We extend results on dichotomy and contractiveness to the case of time-varying descriptor systems. The main tool in our derivations is a new mixed direct/inverse-time Riccati equation.
Vlad Ionescu, Cristian Oara
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Structural Stability for the Riccati Equation
SIAM Journal on Control, 1975The problem of assigning traffic in a multiserver system, where customer-server relationships are determined beforehand, can be regarded as a problem in system design. This is done, and designs are identified which lead to optimization of several alternative criteria.
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ON THE THEORY OF THE MATRIX RICCATI EQUATION
Mathematics of the USSR-Sbornik, 1992See the review Zbl 0747.49006.
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