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80 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ
poles, or a zero D term. Generating random systems is useful for simulating systems
with unknown subsystems.
Specialized Xµ functions are provided for useful manipulations of the state. For example
transforming the A matrix to a real valued, 2 × 2 block diagonal form; here referred to
as modal form. These state-space functions are tabulated below.
Description Xµ
function
state similarity transform simtransform
state reordering orderstate
transform to modal form modalstate
The simtransform function is can also be used on constant matrices and pdms. Xmath
has a transfer function data object which does not have a uniquely defined state.
Applying simtransform or orderstate to a transfer function data object returns a
warning and an unchanged transfer function. Applying modalstate to a transfer
function gives the appropriate state-space representation. With modalstate it is possible
to specify whether the resulting modes are in ascending or descending magnitude order
and whether or not the unstable modes are ordered separately from the stable ones.
pdm Functions
A wide range of matrix functions can also be applied to pdms. Xµ provides several
additional functions which are often of use in typical control applications.
The function spectrad calculates the spectral radius (maximum magnitude eigenvalue)
of a matrix or pdm.
Xmath provides an interpolation function (interpolate) which does only first order
interpolation. There is also a built-in function, spline, for higher order spline fitting.
Zero order interpolation is often required, particularly for looking at fine details in the
inputs of Dynamic System responses. An additional Xµ interpolation function
(interp) is used for this purpose. This command is also useful for mapping data on an
irregularly spaced domain (from experiments for example) to a regular domain.
Simple decimation is easily performed on pdms by direct indexing. The following
example illustrates this.