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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 systems theory, a realization of a state ... because the control ... where is the state-transition matrix associated with the realization. [1] System ...
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.
In control theory, we may need to find out whether or not a system such as ... is the state transition matrix of ˙ = (), is ...
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.
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, the observability and controllability of a linear system are mathematical duals. ... where is the state-transition matrix. It is possible to ...