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13 relations: Aleksandr Lyapunov, Algebraic Riccati equation, Conformable matrix, Conjugate transpose, Control theory, Hermitian matrix, Kalman filter, Kronecker product, Lyapunov function, Lyapunov stability, Optimal control, Positive-definite matrix, Sylvester equation.
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (Алекса́ндр Миха́йлович Ляпуно́в,; – November 3, 1918) was a Russian mathematician, mechanician and physicist.
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Algebraic Riccati equation
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time.
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Conformable matrix
In mathematics, a matrix is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.).
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Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
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Control theory
Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Kalman filter
Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe.
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Kronecker product
In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.
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Lyapunov function
In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE.
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Lyapunov stability
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.
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Optimal control
Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.
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Positive-definite matrix
In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.
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Sylvester equation
In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: Then given matrices A,B, and C, the problem is to find the possible matrices X that obey this equation.
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