Manipulation of generalized state-space (descriptor) system representations
Julia 1.5 and higher.
How to install
pkg> add DescriptorSystems pkg> test DescriptorSystems
DescriptorSystems.jl is a collection of Julia functions for numerical computations related to generalized state-space (descriptor) system representations in the continuous-time form
Edx(t)/dt = Ax(t) + Bu(t) , y(t) = Cx(t) + Du(t) ,
or in the discrete-time form
Ex(t+1) = Ax(t) + Bu(t) , y(t) = Cx(t) + Du(t) ,
y(t) are the system state vector, system input vector and system output vector, respectively, and
t is the continuous or discrete time variable.
This collection also allows the operation on and manipulation of rational and polynomial matrices via their descriptor system realizations.
The functionality of many of the implemented functions parallel or even extend the functionality of the
Control System Toolbox of MATLAB and is similar to that of the
DSTOOLS collection of tools. The underlying computational functions are based on the
Many of the functions implement the computational procedures described in Chapter 10 of the book:
- Andreas Varga, "Solving Fault Diagnosis Problems - Linear Synthesis Techniques", vol. 84 of Studies in Systems, Decision and Control, Springer International Publishing, xxviii+394, 2017.
This book provides additional information on the mathematical background on rational matrices and descriptor systems, and gives detailed descriptions of most of the underlying procedures.
The current version of the package includes the following categories of functions:
Building descriptor system state-space models
Building rational transfer function input-output models
Basic operations on descriptor system models
Basic conversions of descriptor system models
Interconnecting descriptor system models
Simplification of descriptor system models
Descriptor system analysis
Factorization of descriptor system transfer function matrices
Advanced operations on transfer function matrices via their descriptor system realizations
Solution of model-matching problems
Future developments will address support for several new classes of generalized LTI systems types (e.g., for polynomial system models).