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In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. [1] The matrix relates the outputs of the system to its inputs.
A transfer matrix can be obtained for any linear system to analyze its dynamics and other properties; each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
Consequently, () is a matrix with the dimension which contains transfer functions for each input output combination. Due to the simplicity of this matrix notation, the state-space representation is commonly used for multiple-input, multiple-output systems.
The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:
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. This should result in the following form:
In applied mathematics, the Rosenbrock system matrix or Rosenbrock's system matrix of a linear time-invariant system is a useful representation bridging state-space representation and transfer function matrix form. It was proposed in 1967 by Howard H. Rosenbrock. [1]
In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory.
Transfer-matrix method (statistical mechanics), a mathematical technique used to write the partition function into a simpler form. Transfer-matrix method (optics), a method to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. Ray transfer matrix analysis in geometric optics, a mathematical method for ...