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Related papers: A note on Riccati matrix difference equations

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In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…

Optimization and Control · Mathematics 2021-02-02 Paolo Acquistapace , Francesca Bucci

Differential algebraic Riccati equations are at the heart of many applications in control theory. They are time-depent, matrix-valued, and in particular nonlinear equations that require special methods for their solution. Low-rank methods…

Numerical Analysis · Mathematics 2019-12-17 Tobias Breiten , Sergey Dolgov , Martin Stoll

The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…

Mathematical Physics · Physics 2025-10-01 Giuseppe Gaeta , Sebastian Walcher

In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is…

Systems and Control · Electrical Eng. & Systems 2020-06-03 Samir Aberkane , Vasile Dragan

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…

Mathematical Physics · Physics 2017-11-01 L. A. Markovich , R. Grimaudo , A. Messina , H. Nakazato

This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…

Numerical Analysis · Mathematics 2019-04-05 Łukasz Płociniczak

Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller…

Optimization and Control · Mathematics 2017-01-25 Yaguang Yang

The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time invariant control systems. Eigenvalue perturbation theory for the Hamiltonian…

Optimization and Control · Mathematics 2024-04-23 Volker Mehrmann , Hongguo Xu

In this paper we consider a class of conjugate discrete-time Riccati equations (CDARE), arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Recently, we have proved the existence of the…

Optimization and Control · Mathematics 2024-11-05 Chun-Yueh Chiang

The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results obtained are an addition to and based on our earlier work on the…

Functional Analysis · Mathematics 2016-09-02 D. Z. Arov , M. A. Kaashoek , D. R. Pik

Riccati differential equations is the class of first-order and quadratic ordinary differential equations and has various applications in the systems and control theory. In this paper, we analyze a switched Riccati differential equation that…

Dynamical Systems · Mathematics 2022-06-03 Masaki Ogura , Clyde F. Martin

Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…

Numerical Analysis · Mathematics 2023-01-13 Peter Benner , Jan Heiland , Steffen W. R. Werner

We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < {\alpha} < 1. The stability properties…

Numerical Analysis · Mathematics 2018-02-28 Guang-an Zou , Yong Zhou , Bashir Ahmad , Ahmed Alsaedi

The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently Galerkin methods based on Krylov subspaces were developed for the autonomous differential Riccati equation. These…

Numerical Analysis · Mathematics 2019-10-30 Maximilian Behr , Peter Benner , Jan Heiland

Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly…

Classical Analysis and ODEs · Mathematics 2018-12-17 Dorota Mozyrska , Delfim F. M. Torres , Malgorzata Wyrwas

In recent previous work [E. Hansen, T. Stillfjord and T. \r{A}berg, SIAM J. Numer. Anal., to appear], we analyzed the convergence of operator splitting methods applied to operator-valued differential Riccati equations (DRE). In this paper,…

Numerical Analysis · Mathematics 2026-04-29 Eskil Hansen , Tony Stillfjord , Teodor Åberg

Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati…

Numerical Analysis · Mathematics 2024-09-18 Jens Saak , Steffen W. R. Werner

Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic non-linearities. They arise in many different areas, and are particularly important in optimal control of linear quadratic…

Numerical Analysis · Mathematics 2025-04-28 Eskil Hansen , Tony Stillfjord , Teodor Åberg

Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet…

Dynamical Systems · Mathematics 2015-07-09 Cristian Ghiu , Raluca Tuliga , Constantin Udriste , Ionel Tevy

In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that the error of the approximate solution to the operator-valued Riccati equation is…

Numerical Analysis · Mathematics 2024-10-01 James Cheung