Getting Started with MORLAB

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

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

descriptor

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

and second-order form

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

Contents

Model Reduction Routines

As a good starting point, there are demos for all implemented model reduction methods. In the following, the implemented methods are listed, ordered by the system classes they can be applied to:

  1. Continuous-Time Standard Systems (_ct_ss_):
    • Bounded-Real Balanced Truncation (BRBT)
    • Balanced Stochastic Truncation (BST)
    • Balanced Truncation (BT)
    • Frequency-Limited Balanced Truncation (FLBT)
    • H-infinity Balanced Truncation (HINFBT)
    • Hankel-Norm Approximation (HNA)
    • Linear-Quadratic Gaussian Balanced Truncation (LQGBT)
    • Modal Truncation (MT)
    • Positive-Real Balanced Truncation (PRBT)
    • Time-Limited Balanced Truncation (TLBT)
  2. Continuous-Time Descriptor Systems (_ct_dss_):
    • Bounded-Real Balanced Truncation (BRBT)
    • Balanced Stochastic Truncation (BST)
    • Balanced Truncation (BT)
    • Frequency-Limited Balanced Truncation (FLBT)
    • H-infinity Balanced Truncation (HINFBT)
    • Hankel-Norm Approximation (HNA)
    • Linear-Quadratic Gaussian Balanced Truncation (LQGBT)
    • Modal Truncation (MT)
    • Positive-Real Balanced Truncation (PRBT)
    • Time-Limited Balanced Truncation (TLBT)
  3. Continuous-Time Second-Order Systems (_ct_soss_):
    • Balanced Truncation (BT)
    • Frequency-Limited Balanced Truncation (FLBT)
    • Time-Limited Balanced Truncation (TLBT)

The corresponding demos can be found with the naming morlab_demo_[system class]_[abbreviated method], e.g., the demo script of the balanced truncation for standard systems is saved in morlab_demo_ct_ss_bt.m. All demos can be found in the Demos Section. Take also a look into the Contribution Guide for an explanation of the MORLAB naming scheme.

Further Routines

Beside the main routines for model reduction, the toolbox contains several further methods for solving matrix equations and analysing linear systems. A list of all routines can be found in the Function Index or generated by calling help morlab or help morlab-4.0.