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In control theory, the state-transition matrix is a matrix whose product with the state vector at an initial time gives at a later time . The state-transition matrix can be used to obtain the general solution of linear dynamical systems.
In cases where the dimension of the observation vector y is bigger than the dimension of the state space vector x, the information filter can avoid the inversion of a bigger matrix in the Kalman gain calculation at the price of inverting a smaller matrix in the prediction step, thus saving computing time.
In systems theory, a realization of a state ... because the control ... where is the state-transition matrix associated with the realization. [1] System ...
The state-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation given by = + + (), with state vector x, control vector u, vector w of additive disturbances, and fixed matrices A, B, E can be solved by using either the classical method of solving linear differential equations or the Laplace transform method.
In control theory, we may need to find out whether or not a system such as ... is the state transition matrix of ˙ = (), is ...
Control theory [ edit ] The fundamental matrix is used to express the state-transition matrix , an essential component in the solution of a system of linear ordinary differential equations.
In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations.
The state-transition matrix ... this can always be solved for the stacked vector of control vectors if and only if the matrix of matrices at ... and viability theory ...