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

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

Contents

Model Reduction Routines

As a good starting point, there are demos for all main features of the toolbox. In the following, the implemented model reduction 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. Discrete-Time Standard Systems (_dt_ss_):
    • Balanced Truncation (BT)
    • Linear-Quadratic Gaussian Balanced Truncation (LQGBT)
    • Modal Truncation (MT)
  3. 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)
  4. Discrete-Time Descriptor Systems (_dt_dss_):
    • Balanced Truncation (BT)
    • Linear-Quadratic Gaussian Balanced Truncation (LQGBT)
    • Modal Truncation (MT)
  5. Continuous-Time Second-Order Systems (_ct_soss_):
    • Balanced Truncation (BT)
    • Frequency-Limited Balanced Truncation (FLBT)
    • Time-Limited Balanced Truncation (TLBT)

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 given:

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-5.0.