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  2. 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.

  3. Distributed parameter system - Wikipedia

    en.wikipedia.org/wiki/Distributed_parameter_system

    In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equations.

  4. Phase space method - Wikipedia

    en.wikipedia.org/wiki/Phase_space_method

    In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations. The method consists of first rewriting the equations as a system of differential equations that are first-order in time, by introducing additional variables.

  5. State-transition equation - Wikipedia

    en.wikipedia.org/wiki/State-Transition_Equation

    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.

  6. State space (computer science) - Wikipedia

    en.wikipedia.org/wiki/State_space_(computer_science)

    If the size of the state space is finite, calculating the size of the state space is a combinatorial problem. [4] For example, in the Eight queens puzzle, the state space can be calculated by counting all possible ways to place 8 pieces on an 8x8 chessboard. This is the same as choosing 8 positions without replacement from a set of 64, or

  7. Particle filter - Wikipedia

    en.wikipedia.org/wiki/Particle_filter

    These two equations can be viewed as state space equations and look similar to the state space equations for the Kalman filter. If the functions g and h in the above example are linear, and if both W k {\displaystyle W_{k}} and V k {\displaystyle V_{k}} are Gaussian , the Kalman filter finds the exact Bayesian filtering distribution.

  8. Mathematical formulation of quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    However, since s is an unphysical parameter, physical states must be left invariant by "s-evolution", and so the physical state space is the kernel of H − E (this requires the use of a rigged Hilbert space and a renormalization of the norm). This is related to the quantization of constrained systems and quantization of gauge theories. It is ...

  9. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: