outputtype = tf, coeff, zpk, ss, or de

Specifies the subtype of the returned system object.  The default return type is based on the type of the system objects specified in the systems parameter. See the Description section for more details on the return type.

The Subsystem command extracts a subsystem from a system object given a set of selected inputs, outputs and/or states. The input, output, and state variables in the new subsystem are chosen based on the index of their corresponding sets as they appear in the original system object.

The returned system type is the same as the input system type, unless the outputtype option is used, or the input is an ae system type.

In the specific case when the system parameter is an algebraic equation (ae) and no option is specified, the Subsystem command returns a system object in state space form by default. If the algebraic equation system does not have a state space representation, an error is returned. For details on algebraic equation object support by the DynamicSystems package, see DynamicSystems[AlgEquation].

$\mathrm{with}\left(\mathrm{DynamicSystems}\right)\:$

$n≔6\:$$m≔4\:$$p≔3\:$

$\mathrm{A1}≔\mathrm{Matrix}\left(n\,n\,\mathrm{symbol}=a\right)\:$

$\mathrm{B1}≔\mathrm{Matrix}\left(n\,m\,\mathrm{symbol}=b\right)\:$

$\mathrm{C1}≔\mathrm{Matrix}\left(p\,n\,\mathrm{symbol}=c\right)\:$

$\mathrm{D1}≔\mathrm{Matrix}\left(p\,m\,\mathrm{symbol}=d\right)\:$

$\mathrm{sys}≔\mathrm{StateSpace}\left(\mathrm{A1}\,\mathrm{B1}\,\mathrm{C1}\,\mathrm{D1}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{3\; output(s);\; 4\; input(s);\; 6\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u3}\left(t\right)\,\mathrm{u4}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\,\mathrm{y2}\left(t\right)\,\mathrm{y3}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\,\mathrm{x5}\left(t\right)\,\mathrm{x6}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccccc}{a}_{1,1}& a_{1,2}& a_{1,3}& a_{1,4}& a_{1,5}& a_{1,6}\\ a_{2,1}& a_{2,2}& a_{2,3}& a_{2,4}& a_{2,5}& a_{2,6}\\ a_{3,1}& a_{3,2}& a_{3,3}& a_{3,4}& a_{3,5}& a_{3,6}\\ a_{4,1}& a_{4,2}& a_{4,3}& a_{4,4}& a_{4,5}& a_{4,6}\\ a_{5,1}& a_{5,2}& a_{5,3}& a_{5,4}& a_{5,5}& a_{5,6}\\ a_{6,1}& a_{6,2}& a_{6,3}& a_{6,4}& a_{6,5}& a_{6,6}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{cccc}{b}_{1,1}& b_{1,2}& b_{1,3}& b_{1,4}\\ b_{2,1}& b_{2,2}& b_{2,3}& b_{2,4}\\ b_{3,1}& b_{3,2}& b_{3,3}& b_{3,4}\\ b_{4,1}& b_{4,2}& b_{4,3}& b_{4,4}\\ b_{5,1}& b_{5,2}& b_{5,3}& b_{5,4}\\ b_{6,1}& b_{6,2}& b_{6,3}& b_{6,4}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccccc}{c}_{1,1}& c_{1,2}& c_{1,3}& c_{1,4}& c_{1,5}& c_{1,6}\\ c_{2,1}& c_{2,2}& c_{2,3}& c_{2,4}& c_{2,5}& c_{2,6}\\ c_{3,1}& c_{3,2}& c_{3,3}& c_{3,4}& c_{3,5}& c_{3,6}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{cccc}{d}_{1,1}& d_{1,2}& d_{1,3}& d_{1,4}\\ d_{2,1}& d_{2,2}& d_{2,3}& d_{2,4}\\ d_{3,1}& d_{3,2}& d_{3,3}& d_{3,4}\end{array}\right]\end{array}\right.$

$\mathrm{ex\_in}≔\left\{1\,2\,4\right\}\:$

$\mathrm{ex\_out}≔\left\{2\right\}\:$

$\mathrm{ex\_states}≔\left\{1\,3\,6\right\}\:$

$\mathrm{subsys}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\mathrm{ex\_in}\,\mathrm{ex\_out}\,\mathrm{ex\_states}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{subsys}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 3\; input(s);\; 3\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u4}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y2}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x6}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{ccc}{a}_{1,1}& a_{1,3}& a_{1,6}\\ a_{3,1}& a_{3,3}& a_{3,6}\\ a_{6,1}& a_{6,3}& a_{6,6}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{ccc}{b}_{1,1}& b_{1,2}& b_{1,4}\\ b_{3,1}& b_{3,2}& b_{3,4}\\ b_{6,1}& b_{6,2}& b_{6,4}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{ccc}{c}_{2,1}& c_{2,3}& c_{2,6}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{ccc}{d}_{2,1}& d_{2,2}& d_{2,4}\end{array}\right]\end{array}\right.$

$\mathrm{allinputs}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\mathrm{all}\,\left\{1\,2\right\}\,\left\{1\right\}\,\mathrm{outputtype}=\mathrm{de}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{allinputs}\right)$

$\left[\begin{array}{l}\mathbf{Diff.\; Equation}\\ \mathrm{continuous}\\ \mathrm{2\; output(s);\; 4\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u3}\left(t\right)\,\mathrm{u4}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\,\mathrm{y2}\left(t\right)\right]\\ \mathrm{de}\=\{\begin{array}{l}\[\frac{\ⅆ}{\ⅆt}\mathrm{x1}\left(t\right)\=a_{1,1}\mathrm{x1}\left(t\right)+b_{1,1}\mathrm{u1}\left(t\right)+b_{1,2}\mathrm{u2}\left(t\right)+b_{1,3}\mathrm{u3}\left(t\right)+b_{1,4}\mathrm{u4}\left(t\right),\\ \mathrm{y1}\left(t\right)\=c_{1,1}\mathrm{x1}\left(t\right)+d_{1,1}\mathrm{u1}\left(t\right)+d_{1,2}\mathrm{u2}\left(t\right)+d_{1,3}\mathrm{u3}\left(t\right)+d_{1,4}\mathrm{u4}\left(t\right),\\ \mathrm{y2}\left(t\right)\=c_{2,1}\mathrm{x1}\left(t\right)+d_{2,1}\mathrm{u1}\left(t\right)+d_{2,2}\mathrm{u2}\left(t\right)+d_{2,3}\mathrm{u3}\left(t\right)+d_{2,4}\mathrm{u4}\left(t\right)\]\end{array}\end{array}\right.$

$\mathrm{nostates}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\mathrm{ex\_in}\,\mathrm{ex\_out}\,\mathrm{none}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{nostates}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 3\; input(s);\; 0\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u4}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y2}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\right]\\ \mathrm{a}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{ccc}{d}_{2,1}& d_{2,2}& d_{2,4}\end{array}\right]\end{array}\right.$

$\mathrm{dsubsys1}≔\mathrm{Subsystem}\left(\mathrm{sys}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{dsubsys1}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{3\; output(s);\; 4\; input(s);\; 6\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u3}\left(t\right)\,\mathrm{u4}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\,\mathrm{y2}\left(t\right)\,\mathrm{y3}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\,\mathrm{x5}\left(t\right)\,\mathrm{x6}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccccc}{a}_{1,1}& a_{1,2}& a_{1,3}& a_{1,4}& a_{1,5}& a_{1,6}\\ a_{2,1}& a_{2,2}& a_{2,3}& a_{2,4}& a_{2,5}& a_{2,6}\\ a_{3,1}& a_{3,2}& a_{3,3}& a_{3,4}& a_{3,5}& a_{3,6}\\ a_{4,1}& a_{4,2}& a_{4,3}& a_{4,4}& a_{4,5}& a_{4,6}\\ a_{5,1}& a_{5,2}& a_{5,3}& a_{5,4}& a_{5,5}& a_{5,6}\\ a_{6,1}& a_{6,2}& a_{6,3}& a_{6,4}& a_{6,5}& a_{6,6}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{cccc}{b}_{1,1}& b_{1,2}& b_{1,3}& b_{1,4}\\ b_{2,1}& b_{2,2}& b_{2,3}& b_{2,4}\\ b_{3,1}& b_{3,2}& b_{3,3}& b_{3,4}\\ b_{4,1}& b_{4,2}& b_{4,3}& b_{4,4}\\ b_{5,1}& b_{5,2}& b_{5,3}& b_{5,4}\\ b_{6,1}& b_{6,2}& b_{6,3}& b_{6,4}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccccc}{c}_{1,1}& c_{1,2}& c_{1,3}& c_{1,4}& c_{1,5}& c_{1,6}\\ c_{2,1}& c_{2,2}& c_{2,3}& c_{2,4}& c_{2,5}& c_{2,6}\\ c_{3,1}& c_{3,2}& c_{3,3}& c_{3,4}& c_{3,5}& c_{3,6}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{cccc}{d}_{1,1}& d_{1,2}& d_{1,3}& d_{1,4}\\ d_{2,1}& d_{2,2}& d_{2,3}& d_{2,4}\\ d_{3,1}& d_{3,2}& d_{3,3}& d_{3,4}\end{array}\right]\end{array}\right.$

$\mathrm{nsubsys}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\mathrm{none}\,\mathrm{none}\,\mathrm{none}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{nsubsys}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{0\; output(s);\; 0\; input(s);\; 0\; state(s)}\\ \mathrm{inputvariable}\=\left[\right]\\ \mathrm{outputvariable}\=\left[\right]\\ \mathrm{statevariable}\=\left[\right]\\ \mathrm{a}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{}\end{array}\right]\end{array}\right.$

$\mathrm{subsys1}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\left\{1\,2\,3\right\}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{subsys1}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{3\; output(s);\; 3\; input(s);\; 6\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u2}\left(t\right)\,\mathrm{u3}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\,\mathrm{y2}\left(t\right)\,\mathrm{y3}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\,\mathrm{x5}\left(t\right)\,\mathrm{x6}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccccc}{a}_{1,1}& a_{1,2}& a_{1,3}& a_{1,4}& a_{1,5}& a_{1,6}\\ a_{2,1}& a_{2,2}& a_{2,3}& a_{2,4}& a_{2,5}& a_{2,6}\\ a_{3,1}& a_{3,2}& a_{3,3}& a_{3,4}& a_{3,5}& a_{3,6}\\ a_{4,1}& a_{4,2}& a_{4,3}& a_{4,4}& a_{4,5}& a_{4,6}\\ a_{5,1}& a_{5,2}& a_{5,3}& a_{5,4}& a_{5,5}& a_{5,6}\\ a_{6,1}& a_{6,2}& a_{6,3}& a_{6,4}& a_{6,5}& a_{6,6}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{ccc}{b}_{1,1}& b_{1,2}& b_{1,3}\\ b_{2,1}& b_{2,2}& b_{2,3}\\ b_{3,1}& b_{3,2}& b_{3,3}\\ b_{4,1}& b_{4,2}& b_{4,3}\\ b_{5,1}& b_{5,2}& b_{5,3}\\ b_{6,1}& b_{6,2}& b_{6,3}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccccc}{c}_{1,1}& c_{1,2}& c_{1,3}& c_{1,4}& c_{1,5}& c_{1,6}\\ c_{2,1}& c_{2,2}& c_{2,3}& c_{2,4}& c_{2,5}& c_{2,6}\\ c_{3,1}& c_{3,2}& c_{3,3}& c_{3,4}& c_{3,5}& c_{3,6}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{ccc}{d}_{1,1}& d_{1,2}& d_{1,3}\\ d_{2,1}& d_{2,2}& d_{2,3}\\ d_{3,1}& d_{3,2}& d_{3,3}\end{array}\right]\end{array}\right.$

$\mathrm{subsys2}≔\mathrm{Subsystem}\left(\mathrm{sys}\,\left\{1\,3\right\}\,\left\{1\,2\right\}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{subsys2}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{2\; output(s);\; 2\; input(s);\; 6\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\,\mathrm{u3}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\,\mathrm{y2}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\,\mathrm{x5}\left(t\right)\,\mathrm{x6}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccccc}{a}_{1,1}& a_{1,2}& a_{1,3}& a_{1,4}& a_{1,5}& a_{1,6}\\ a_{2,1}& a_{2,2}& a_{2,3}& a_{2,4}& a_{2,5}& a_{2,6}\\ a_{3,1}& a_{3,2}& a_{3,3}& a_{3,4}& a_{3,5}& a_{3,6}\\ a_{4,1}& a_{4,2}& a_{4,3}& a_{4,4}& a_{4,5}& a_{4,6}\\ a_{5,1}& a_{5,2}& a_{5,3}& a_{5,4}& a_{5,5}& a_{5,6}\\ a_{6,1}& a_{6,2}& a_{6,3}& a_{6,4}& a_{6,5}& a_{6,6}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{cc}{b}_{1,1}& b_{1,3}\\ b_{2,1}& b_{2,3}\\ b_{3,1}& b_{3,3}\\ b_{4,1}& b_{4,3}\\ b_{5,1}& b_{5,3}\\ b_{6,1}& b_{6,3}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccccc}{c}_{1,1}& c_{1,2}& c_{1,3}& c_{1,4}& c_{1,5}& c_{1,6}\\ c_{2,1}& c_{2,2}& c_{2,3}& c_{2,4}& c_{2,5}& c_{2,6}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{cc}{d}_{1,1}& d_{1,3}\\ d_{2,1}& d_{2,3}\end{array}\right]\end{array}\right.$

The DynamicSystems[Subsystem] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.