A special property of the matrix Riccati equation
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In this paper, the Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, and it is shown that, subject to a continuity restriction, the RDE is unique among comparable equations in possessing this property.Abstract:
In the domain of real symmetric matrices ordered by the positive definiteness criterion, the symmetric matrix Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, Here is is shown that, subject to a continuity restriction, the Riccati equation is unique among comparable equations in possessing this property.read more
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A survey of nonsymmetric Riccati equations
TL;DR: In this article, the authors survey recent and also older results on nonsymmetric matrix Riccati differential equations and their corresponding algebraic variants, and cite various applications connected with matrix RICCati equations.
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Affine Processes on Positive Semidefinite Matrices
TL;DR: In this paper, the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices is provided, and a large range of useful applications in finance, including multi-asset option pricing with stochastic volatility and correlation structures.
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Affine processes on positive semidefinite matrices
TL;DR: In this article, the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices is provided, motivated by a large and growing use of matrix-valued affine process in finance, including multi-asset option pricing with stochastic volatility and correlation structures.
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Time-varying discrete Riccati equation: some monotonicity results
Gerhard Freiling,Vlad Ionescu +1 more
TL;DR: Using a Fre´chet derivative based approach some monotonicity and comparison results concerning the solutions of the time-varying discrete time Riccati equation are obtained as discussed by the authors.
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Adaptive Disturbance Torque Estimation for Orbiting Spacecraft Using Recursive Least-Squares Methods
TL;DR: A novel disturbance torque estimator for an orbiting spacecraft by using the adaptive least-squares parameter estimation technique, and it is shown that the convergent rate for estimation errors can be made at the same level as the forgetting factor.
References
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TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
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Optimal control: An introduction to the theory and ITs applications
Stephen Kahne,E. Lee +1 more
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Optimal Control. An Introduction to the Theory and Its Applications
Michael Athans,Peter Falb +1 more
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On the equivalence between matrix riccati equations and Fredholm resolvents
TL;DR: It is shown that the solution to every matrix Riccati equation can be generated by the resolvent of a certain Fredholm integral operator and, conversely, this Resolvent can be determined from the corresponding Riccatis solution.