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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.
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.
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 ...
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 ...
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
Thus the set of all states of M with the weak-* topology forms a compact Hausdorff space, known as the state space of M. In the C*-algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i.e. mappings from physical observables (self-adjoint elements of the C*-algebra) to their expected ...
State/Space theory constitutes a new branch of social and political geography in which the issues of space as a geographic element are considered for their influence on political relationships and outcomes. [1] Leading scholars include Neil Brenner at the Harvard Graduate School of Design, and Bob Jessop at Lancaster University in England ...
For computational purposes, a short form of the Rosenbrock system matrix is more appropriate [2] and given by ().The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, where it is also referred to as packed form; see command pck in MATLAB. [3]