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Matrix difference equation

A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example,

Nonlinear matrix difference equations: Riccati equations, Solution of the first-order case & Stability of the first-order case

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Nonlinear matrix difference equations: Riccati equations

Linear-quadratic-Gaussian controlRiccati equationExogenousQuadraticCost function
9 related topics

Solution of the first-order case

Initial conditionMathematical inductionEigenvalues and eigenvectorsEigenvectorsDiagonal matrix
5 related topics

Stability of the first-order case

StableEigenvaluesAbsolute valueSpectral radius
4 related topics

Nonhomogeneous first-order case and the steady state

Identity matrixInvertible
2 related topics

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Nonhomogeneous first-order case and the steady state

Stability of the first-order case

Solution of the first-order case

Extracting the dynamics of a single scalar variable from a first-order matrix system

Solution and stability of higher-order cases

Nonlinear matrix difference equations: Riccati equations

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Matrix difference equation

Nodes36
Edges35
Triples14
Avg. degree1.94
Density0.055556
Components1

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Matrix difference equation

Top relations

related to Nonlinear matrix difference equations: Riccati equations · 7
Matrix difference equation → Gaussian, In, Riccati, See, The, This, This Riccati
related to Solution and stability of higher-order cases · 3
Matrix difference equation → For, Matrix, This
related to Nonhomogeneous first-order case and the steady state · 2
Matrix difference equation → An, The
is a · 1
Matrix difference equation → difference equation in which the value of a vector
related to Stability of the first-order case · 1
Matrix difference equation → The

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Important terminology

equation matrix difference vector eigenvalues matrices time riccati first-order value solution variable form variables displaystyle mathbf system also stable terms

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SubjectPredicateObjectConfidenceSrc
Matrix difference equationis adifference equation in which the value of a vector0.90text
Matrix difference equationrelated to Nonhomogeneous first-order case and the steady stateAn0.60section
Matrix difference equationrelated to Nonhomogeneous first-order case and the steady stateThe0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsIn0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsGaussian0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsThis0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsRiccati0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsThis Riccati0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsThe0.60section
Matrix difference equationrelated to Nonlinear matrix difference equations: Riccati equationsSee0.60section
Matrix difference equationrelated to Solution and stability of higher-order casesMatrix0.60section
Matrix difference equationrelated to Solution and stability of higher-order casesFor0.60section

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