Library Modelica_LinearSystems2 is a Modelica package providing different representations of linear, time invariant differential and difference equation systems. For example, record StateSpace defines a linear time invariant differential equation system in state space form:
der(x) = A * x + B * u y = C * x + D * u
Operators are overloaded to work conveniently with these system descriptions in an interactive environment, e.g. to multiply transfer functions or to operate on complex numbers. About 180 functions are provided to operate on these data structures, e.g. to compute eigenvalues, zeros, step responses, to design poleplacement and LQG controllers, to plot step responses, frequency responses, eigenvalues, to convert between different description forms, or to generate a linear system description by linearization of a Modelica model.
Furthermore, in subpackage Controller about 20 input/output blocks of linear systems are provided that are based on the different representation forms, e.g. PID, StateSpace, Filter blocks. A unique feature of these blocks is that it is very convenient to quickly switch between a continuous and a discrete block representation. Also, templates are provided to quickly builtup standard controller structures.
For an introduction, have especially a look at:
It is planned to include this library in a future version of the Modelica Standard Library.
Licensed by DLR under the Modelica License 2 

Copyright © 20052012, DLR Institute of Robotics and Mechatronics  
Copyright © 20122015, DLR Institute of System Dynamics and Control 
This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the Modelica license 2, see the license conditions (including the disclaimer of warranty) in the User's Guide or at http://www.Modelica.org/licenses/ModelicaLicense2.
Name  Description 

UsersGuide  User's Guide 
ModelAnalysis  Package of functions to perform analysis on Modelica models (nonlinear models are linearized) 
Examples  Package of examples to demonstrate the usage of functions from the library 
StateSpace  Continuous state space description of a linear, time invariant differential equation system (data + operations) 
ZerosAndPoles  Continuous zeros and poles description of a single input, single output system (data + operations) 
TransferFunction  Continuous transfer function description of a single input, single output system (data + operations) 
DiscreteStateSpace  Discrete state space description of a linear, time invariant difference equation system (data + operations) 
DiscreteZerosAndPoles  Discrete zeros and poles description of a single input, single output system (data + operations) 
DiscreteTransferFunction  Discrete transfer function description of a single input, single output system (data + operations) 
Controller  Package of continuous and discrete input/output blocks 
Math  Package of additional functions for Modelica.Math 
Utilities  Package of utility elements used in the library 
Internal  Package of internal utilities of the library (for advanced users only) 
Types  Package of type definitions 
Records  Records, especially to build menus 
WorkInProgress  Package for developments and internal models 