We offer some MATLAB™ Toolboxes:

Descriptor Systems Toolbox

This MATLAB toolbox has been developed in order to

• enhance the MATLAB Control Toolbox by handling the most general linear system representations
• solve in a numerically reliable way many standard control problems by using descriptor system techniques
• manipulate in a numerically reliable way rational and polynomial matrices
• extend the capabilities of basic MATLAB with matrix pencil methods

The DESCRIPTOR SYSTEMS Toolbox for MATLAB is partly based on RASP-DESCRIPT routines implemented in Fortran 77 and partly based on the control software library SLICOT. The underlying algorithms encompass computations like the determination of complete Kronecker structure of linear pencils, generalized pole assignment and stabilization, model conversions (descriptor state-space to rational/polynomial representations), general rational factorisations (inner-outer, normalized coprime), generalized inverses (left/right, week, Moore-Penrose), solution of systems of equations with rational matrices etc. This package illustrates the new trend in CACSD to employ high quality, robust control software written in high level languages (e.g., Fortran) in user-friendly environments like MATLAB via appropriate gateways (mex-files).

Take a look here for a more detailed description.

SLICOT Basic Systems and Control Toolbox

SLICOT Basic Systems and Control Toolbox includes SLICOT-based MATLAB and Fortran tools for solving efficiently and reliably various basic computational problems for linear time-invariant multivariable systems analysis and synthesis. Standard and generalised (descriptor) state space systems are covered.

The main functionalities of the toolbox include:

• similarity and equivalence transformations for standard and descriptor systems
• essential computations with structured matrices, including
  
  
  • eigenvalues of a Hamiltonian matrix
  • Periodic Hessenberg and periodic Schur decompositions
  • computations with (block) Toeplitz matrices and systems
    
    
• analysis of standard and descriptor systems
• solution of Lyapunov and Riccati equations with condition estimation
• coprime factorization and spectral decomposition of transfer-function matrices

Take a look here for a more detailed description.

SLICOT Model and Controler Reduction Toolbox

SLICOT Model and Controller Reduction Toolbox includes SLICOT-based MATLAB and Fortran tools for computing reduced-order linear models and controllers. The toolbox employs theoretically sound and numerically reliable and efficient techniques, including Balance & Truncate, singular perturbation approximation, balanced stochastic truncation, frequency-weighting balancing, Hankel-norm approximation, coprime factorization, etc.

The main functionalities of the toolbox include:

• order reduction for continuous-time and discrete-time multivariable models and controllers
• order reduction for stable or unstable models/controllers
• additive error model reduction
• relative error model and controller reduction
• frequency-weighted reduction with special stability/performance enforcing weights
• coprime factorization-based reduction of state feedback and observer-based controllers

Take a look here for a more detailed description.

SLICOT System Identification Toolbox

SLICOT System Identification Toolbox includes SLICOT-based MATLAB and Fortran tools for linear and Wiener-type, time-invariant discrete-time multivariable systems. Subspace-based approaches MOESP - Multivariable Output-Error state SPace identification, N4SID - Numerical algorithms for Subspace State Space System IDentification, and their combination, are used to identify linear systems, and to initialize the parameters of the linear part of a Wiener system. All parameters of a Wiener system are then estimated using a specialized Levenberg-Marquardt algorithm.
The main functionalities of the toolbox include:

• identification of linear discrete-time state space systems (A, B, C, D)
• identification of state and output (cross-)covariance matrices for such systems
• estimation of the associated Kalman gain matrix
• estimation of the initial state
• conversion from/to a state-space representation to the output normal form parameterization
• identification of discrete-time Wiener systems
• computation of the output response of Wiener systems.

Take a look here for a more detailed description.

Toolbox for the Numerical Solution of Differential-Algebraic Equations

The purpose of this MATLAB toolbox is the numerical solution of systems of linear and nonlinear differention-algebraic equations (DAEs) with variable coefficients of arbitrary index.  It contains the subroutines

• GENDA (GEneral Linear Differential-Algebraic equation solver) and
• GELDA (GEneral Nonlinear Differential-Algebraic equation solver).

Both routines are Numerically reliable state-of-the-art solvers providing solutions for under- and overdetermined Systems.
This toolbox features symbolic differentiation (Symbolic Math Toolbox required). Other features of the toolbox include

• the computation of characteristic values
• the computation of consistent initial values in the least square sense (Optimization Toolbox required)
• many parameters that enable the user to customize the solvers to certain problems.

Information

Do you have questions concerning MATLAB toolboxes ? Don´t hesitate to contact us.