Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Guide for ZigangPan`LinearSystems`
A guide to all the functions defined in the paclet.
— check a given variable is in the special system representation (i.e., the ten-item list format).
— Do various operations on a LTI system in the special ten-item format. Such as:
View -- view the system in a table like format
Organize -- sort the state, input, and output names and list the system in a more organized way
Organize and View -- do both of above
Add active inputs
Add active outputs
Drop active inputs
Drop active outputs
Set active inputs
Set active outputs
Add control inputs
Drop control inputs
Add disturbance inputs
Drop disturbance inputs
....
State transformation -- do state transformation using the transformation matrix provided. old state = transformation matrix. new state.
View -- view the system in a table like format
Organize -- sort the state, input, and output names and list the system in a more organized way
Organize and View -- do both of above
Add active inputs
Add active outputs
Drop active inputs
Drop active outputs
Set active inputs
Set active outputs
Add control inputs
Drop control inputs
Add disturbance inputs
Drop disturbance inputs
....
State transformation -- do state transformation using the transformation matrix provided. old state = transformation matrix. new state.
— build a bigger system that consists of two LTI systems in block diagonal composition.
— concatenate two LTI systems in special format.
— parallel interconnect two LTI systems in special format such that they share the common active inputs.
— simulate an LTI system in feedback with a linear controller and a disturbance system.
— generate an empty LTI system in special format.
— generate a LTI system in special format that represents a gain given by the matrix.
— check the controllability of a pair (A,B), determine the dimension of the controllable subspace, determine the controllability indices for each of the control input terminal, and gives the transformation that transform the pair to the controller canonical form.
— check the observability of a pair (A,C), determine the dimension of the observable subspace, determine the observability indices for each of the output channels, and gives the transformation that transform the pair to the observer canonical form.
— check the controllability of an LTI system in special format, determine the dimension of the controllable subspace, determine the controllability indices for each of the control input terminal, and gives the transformation that transform the pair to the controller canonical form, and the LTI system representation of the controller canonical form.
— check the observability of an LTI system in special format, determine the dimension of the observable subspace, determine the observability indices for each of the output channels, and gives the transformation that transform the pair to the observer canonical form, and the LTI system representation of the observer canonical form.
— determine the stablizability of a pair (A,B).
— determine the detectability of a pair (A,C).
— solve a Lyapunov equation.
— solve a Riccati equation.
— solve a generalized Riccati equation using Hamiltonian method.
— solve a discrete-time Lyapunov equation.
— solve a discrete-time Riccati equation.
— calculate the relative degrees of a quadruple (A,B,C,D) and determine whether it admits vector relative degree.
— do dynamic extension on an LTI system in special format to reach (uniform) vector relative degree.
— similar to observercanonicalform, but also checks whether the observer canonical form is strict.
— will extend a system such that it admits the strict observer canonical form. But does not guarantee the extended system admits uniform observability indices.
— will extend a system to one with uniform observability indices and therefore admits the strict observer canonical form.
— calculates the zero dynamics canonical form of the system. Requires the system to admit vector relative degrees.
— calculates the extended zero dynamics canonical form of the system.
— calculates the extended zero dynamics canonical form of the system, and will dynamically extend (independent of unknown parameters) and/or add integrator on the output of the system to result in an extended system with uniform vector relative degree.
— returns the design model for a parametrized MIMO LTI system with uniform relative degree of zero and is also in strict observer canonical form.
Basic system functions:
Functions operating on system matrices:
System functions operating on a system:
Matrix equation solvers:
Functions for adaptive control design purposes:
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