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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. Behavioral modeling - Wikipedia

    en.wikipedia.org/wiki/Behavioral_modeling

    The behavioral approach to systems theory and control theory was initiated in the late-1970s by J. C. Willems as a result of resolving inconsistencies present in classical approaches based on state-space, transfer function, and convolution representations.

  4. Distributed parameter system - Wikipedia

    en.wikipedia.org/wiki/Distributed_parameter_system

    In discrete-time the transfer function is given in terms of the state-space parameters by + = and it is holomorphic in a disc centered at the origin. [4] In case 1/ z belongs to the resolvent set of A (which is the case on a possibly smaller disc centered at the origin) the transfer function equals D + C z ( I − z A ) − 1 B {\displaystyle D ...

  5. Takens's theorem - Wikipedia

    en.wikipedia.org/wiki/Takens's_theorem

    The state space of the dynamical system is a ν-dimensional manifold M. The dynamics is given by a smooth map:. Assume that the dynamics f has a strange attractor with box counting dimension d A. Using ideas from Whitney's embedding theorem, A can be embedded in k-dimensional Euclidean space with

  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. Realization (systems) - Wikipedia

    en.wikipedia.org/wiki/Realization_(systems)

    Any given transfer function which is strictly proper can easily be transferred into state-space by the following approach (this example is for a 4-dimensional, single-input, single-output system)): Given a transfer function, expand it to reveal all coefficients in both the numerator and denominator.

  8. Subspace identification method - Wikipedia

    en.wikipedia.org/wiki/Subspace_identification_method

    In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to ...

  9. Hankel matrix - Wikipedia

    en.wikipedia.org/wiki/Hankel_matrix

    Hankel matrices are formed when, given a sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. [3] The singular value decomposition of the Hankel matrix provides a means of computing the A , B , and C matrices which define the state-space realization. [ 4 ]