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  2. State-transition matrix - Wikipedia

    en.wikipedia.org/wiki/State-transition_matrix

    The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .

  3. State-transition table - Wikipedia

    en.wikipedia.org/wiki/State-transition_table

    Now if the machine is in the state S 1 and receives an input of 0 (first column), the machine will transition to the state S 2. In the state diagram, the former is denoted by the arrow looping from S 1 to S 1 labeled with a 1, and the latter is denoted by the arrow from S 1 to S 2 labeled with a 0.

  4. State-space representation - Wikipedia

    en.wikipedia.org/wiki/State-space_representation

    The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.

  5. Kalman filter - Wikipedia

    en.wikipedia.org/wiki/Kalman_filter

    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.

  6. Controllability Gramian - Wikipedia

    en.wikipedia.org/wiki/Controllability_Gramian

    The matrix () = = () is nonsingular for any >. ... is the state transition matrix of ˙ = (), is nonsingular. Again, we have a similar method to determine if a system ...

  7. Stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Stochastic_matrix

    In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. [1] [2]: 10 It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix.

  8. UML state machine - Wikipedia

    en.wikipedia.org/wiki/UML_state_machine

    Figure 7: State roles in a state transition. In UML, a state transition can directly connect any two states. These two states, which may be composite, are designated as the main source and the main target of a transition. Figure 7 shows a simple transition example and explains the state roles in that transition.

  9. Fundamental matrix (linear differential equation) - Wikipedia

    en.wikipedia.org/wiki/Fundamental_matrix_(linear...

    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. [3]