A Note on Riccati Matrix Difference Equations

DOI10.1137/21M1437226zbMath1495.39003arXiv2107.12918OpenAlexW3186857508MaRDI QIDQ5081086

Emma Horton, Pierre Del Moral

Publication date: 1 June 2022

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12918

zbMATH Keywords

Floquet theoryLyapunov equationsGramian matrixRiccati matrix difference equationsdiscrete time algebraic Riccati equationmatrix positive definite mapssemigroup duality formulaSherman-Morrison-Woodbury inversion identity

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Discrete version of topics in analysis (39A12) Linear difference equations (39A06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A generalization of the Sherman-Morrison-Woodbury formula
• A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems
• Popov-Belevitch-Hautus type controllability tests for linear complementarity systems
• Periodic systems. Filtering and control
• Monotonicity and stabilizability properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples
• Stochastic models, estimation, and control. Vol. 1
• Sets of matrices all infinite products of which converge
• A comparison theorem for matrix Riccati difference equations
• The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate
• Matrix Riccati equations in control and systems theory
• A Taylor expansion of the square root matrix function
• A perturbation analysis of stochastic matrix Riccati diffusions
• Employing the algebraic Riccati equation for a parametrization of the solutions of the finite-horizon LQ problem: the discrete-time case
• Stochastic processes and filtering theory
• Infinite-Horizon Linear-Quadratic Control by Forward Propagation of the Differential Riccati Equation [Lecture Notes]
• Updating the Inverse of a Matrix
• On Deriving the Inverse of a Sum of Matrices
• An algorithm for solving the matrix equationX = FXF^T+S
• Array algorithms for H/sup ∞/ estimation
• On the Stability of Kalman--Bucy Diffusion Processes
• Hermitian solutions of the discrete-time algebraic Riccati equation
• The set of positive semidefinite solutions of the algebraic Riccati equation of discrete-time optimal control
• A Negative Definite Equilibrium and Its Induced Cone of Global Existence for the Riccati Equation
• Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix
• An Inverse Matrix Adjustment Arising in Discriminant Analysis
• Enlargement Methods for Computing the Inverse Matrix
• An explicit Floquet-type representation of Riccati aperiodic exponential semigroups