Getting Started with MORLAB

The toolbox includes several methods for model reduction of linear dynamical systems in continuous-time standard

$\setlength\arraycolsep{2pt} \begin{array}{rl} \dot{x}(t) & = Ax(t) + Bu(t),\\ y(t) & = Cx(t) + Du(t), \end{array}$

discrete-time standard

$\setlength\arraycolsep{2pt} \begin{array}{rl} x_{k+1} & = Ax_{k} + Bu_{k},\\ y_{k} & = Cx_{k} + Du_{k}, \end{array}$

continuous-time descriptor

$\setlength\arraycolsep{2pt} \begin{array}{rl} E\dot{x}(t) & = Ax(t) + Bu(t),\\ y(t) & = Cx(t) + Du(t), \end{array}$

discrete-time descriptor

$\setlength\arraycolsep{2pt} \begin{array}{rl} Ex_{k+1} & = Ax_{k} + Bu_{k},\\ y_{k} & = Cx_{k} + Du_{k}, \end{array}$

and second-order form

$\setlength\arraycolsep{2pt} \begin{array}{rr} M\ddot{x}(t) = & -Kx(t) - \phantom{_{v}}E\dot{x}(t) + B_{u}u(t),\\ y(t) = & C_{p}x(t) + C_{v}\dot{x}(t) + \phantom{_{u}}Du(t). \end{array}$

Model Reduction Routines
Further Routines

Model Reduction Routines

As a starting point, there are demos for all main features of the toolbox. In the following, the implemented model reduction procedures are listed. Note that these are top level routines that automatically determine the given system type and apply the corresponding model reduction routines; not all methods are available for all different kinds of systems:

Continuous-time systems:
- Bounded-Real Balanced Truncation (BRBT): ml_ct_brbt
- Balanced Stochastic Truncation (BST): ml_ct_bst
- Balanced Truncation (BT): ml_ct_bt
- Frequency-Limited Balanced Truncation (FLBT): ml_ct_flbt
- H-infinity Balanced Truncation (HINFBT): ml_ct_hinfbt
- Krylov subspace methods: ml_ct_krylov
- Hankel-Norm Approximation (HNA): ml_ct_hna
- Linear-quadratic Gaussian Balanced Truncation (LQGBT): ml_ct_lqgbt
- Modal Truncation (MT): ml_ct_mt
- Positive-Real Balanced Truncation (PRBT): ml_ct_prbt
- Time-Limited Balanced Truncation (TLBT): ml_ct_tlbt
- Two-step model reduction: ml_ct_twostep_mor
Discrete-time systems:
- Balanced Truncation (BT): ml_dt_bt
- Krylov subspace methods: ml_dt_krylov
- Linear-Quadratic Gaussian Balanced Truncation (LQGBT): ml_dt_lqgbt
- Modal Truncation (MT): ml_dt_mt
- Two-step model reduction: ml_dt_twostep_mor

As stated above, there is a demo script for each of the main features, which can be used as a starting point. All of them can be found in the Demos Section. The following demos are available:

Model reduction methods in MORLAB (morlab_demo_mor_default.m)
Model reduction for second-order systems (morlab_demo_mor_secondorder.m)
Matrix equation solvers (morlab_demo_equation_solvers.m)
Additive decomposition (morlab_demo_additive_decomposition.m)
Partial Stabilization (morlab_demo_partial_stabilization.m)
Frequency evaluation and visualization (morlab_demo_frequency_evaluation.m)
Time evaluation and visualization (morlab_demo_time_evaluation.m)
Option Constructor Function ml_morlabopts (morlab_demo_morlabopts.m)

Further Routines

A complete list of routines with short descriptions can be found in the Function Index or generated by calling help morlab or help morlab-6.0.

Getting Started with MORLAB

Contents

Model Reduction Routines

Further Routines