$\mathrm{sys}:=\mathrm{TransferFunction}\left(\frac{A}{s\+\mathrm{\ω}}\,\mathrm{parameters}\=\left[A\=1\,\mathrm{\ω}\=2\right]\right)\:$

$\mathrm{MagnitudePlot}\left(\mathrm{sys}\right)$

$\mathrm{MagnitudePlot}\left(\mathrm{sys}\,\mathrm{parameters}\=\left[A\=100\right]\right)$

AppendConnect: Create the equivalent system representation of two or more system objects combined by appending their inputs and outputs.

FeedbackConnect: Create the equivalent system representation of one or two system objects with positive or negative feedback connection.

ParallelConnect: Create the equivalent system representation of two or more system objects connected in parallel.

SeriesConnect: Create the equivalent system representation of two or more system objects connected in series.

$\mathrm{sys1}:=\mathrm{StateSpace}\left(\mathrm{usesymbols}\,\mathrm{numstates}\=2\,\mathrm{numinputs}\=1\,\mathrm{numoutputs}\=1\,\mathrm{symbols}\=\left[\mathrm{A1}\,\mathrm{B1}\,\mathrm{C1}\,\mathrm{D1}\right]\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys1}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 2\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cc}{\mathrm{A1}}_{1,1}& {\mathrm{A1}}_{1,2}\\ {\mathrm{A1}}_{2,1}& {\mathrm{A1}}_{2,2}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}{\mathrm{B1}}_{1,1}\\ {\mathrm{B1}}_{2,1}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cc}{\mathrm{C1}}_{1,1}& {\mathrm{C1}}_{1,2}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}{\mathrm{D1}}_{1,1}\end{array}\right]\end{array}\right.$

$\mathrm{sys2}:=\mathrm{StateSpace}\left(\mathrm{usesymbols}\,\mathrm{numstates}\=2\,\mathrm{numinputs}\=1\,\mathrm{numoutputs}\=1\,\mathrm{symbols}\=\left[\mathrm{A2}\,\mathrm{B2}\,\mathrm{C2}\,\mathrm{D2}\right]\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys2}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 2\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cc}{\mathrm{A2}}_{1,1}& {\mathrm{A2}}_{1,2}\\ {\mathrm{A2}}_{2,1}& {\mathrm{A2}}_{2,2}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}{\mathrm{B2}}_{1,1}\\ {\mathrm{B2}}_{2,1}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cc}{\mathrm{C2}}_{1,1}& {\mathrm{C2}}_{1,2}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}{\mathrm{D2}}_{1,1}\end{array}\right]\end{array}\right.$

$\mathrm{sys\_series}:=\mathrm{SeriesConnect}\left(\left[\mathrm{sys1}\,\mathrm{sys2}\right]\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys\_series}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 4\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccc}{\mathrm{A1}}_{1,1}& {\mathrm{A1}}_{1,2}& 0& 0\\ {\mathrm{A1}}_{2,1}& {\mathrm{A1}}_{2,2}& 0& 0\\ {\mathrm{B2}}_{1,1}{\mathrm{C1}}_{1,1}& {\mathrm{B2}}_{1,1}{\mathrm{C1}}_{1,2}& {\mathrm{A2}}_{1,1}& {\mathrm{A2}}_{1,2}\\ {\mathrm{B2}}_{2,1}{\mathrm{C1}}_{1,1}& {\mathrm{B2}}_{2,1}{\mathrm{C1}}_{1,2}& {\mathrm{A2}}_{2,1}& {\mathrm{A2}}_{2,2}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}{\mathrm{B1}}_{1,1}\\ {\mathrm{B1}}_{2,1}\\ {\mathrm{B2}}_{1,1}{\mathrm{D1}}_{1,1}\\ {\mathrm{B2}}_{2,1}{\mathrm{D1}}_{1,1}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccc}{\mathrm{D2}}_{1,1}{\mathrm{C1}}_{1,1}& {\mathrm{D2}}_{1,1}{\mathrm{C1}}_{1,2}& {\mathrm{C2}}_{1,1}& {\mathrm{C2}}_{1,2}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}{\mathrm{D2}}_{1,1}{\mathrm{D1}}_{1,1}\end{array}\right]\end{array}\right.$

$\mathrm{sys\_parallel}:=\mathrm{ParallelConnect}\left(\left[\mathrm{sys1}\,\mathrm{sys2}\right]\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys\_parallel}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 4\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\,\mathrm{x4}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cccc}{\mathrm{A1}}_{1,1}& {\mathrm{A1}}_{1,2}& 0& 0\\ {\mathrm{A1}}_{2,1}& {\mathrm{A1}}_{2,2}& 0& 0\\ 0& 0& {\mathrm{A2}}_{1,1}& {\mathrm{A2}}_{1,2}\\ 0& 0& {\mathrm{A2}}_{2,1}& {\mathrm{A2}}_{2,2}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}{\mathrm{B1}}_{1,1}\\ {\mathrm{B1}}_{2,1}\\ {\mathrm{B2}}_{1,1}\\ {\mathrm{B2}}_{2,1}\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cccc}{\mathrm{C1}}_{1,1}& {\mathrm{C1}}_{1,2}& {\mathrm{C2}}_{1,1}& {\mathrm{C2}}_{1,2}\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}{\mathrm{D1}}_{1,1}+{\mathrm{D2}}_{1,1}\end{array}\right]\end{array}\right.$

$\mathrm{sysd}:=\mathrm{TransferFunction}\left(\frac{1}{z\+a}\,\mathrm{discrete}\,\mathrm{parameters}\=\left[a\=3\right]\right)\:$

$\mathrm{sysc1}:=\mathrm{ToContinuous}\left(\mathrm{sysd}\,\mathrm{method}\=\mathrm{forward}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sysc1}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(s\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(s\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{1}{s+1+a}\end{array}\right.$

$\mathrm{sysc2}:=\mathrm{ToContinuous}\left(\mathrm{sysd}\,\mathrm{method}\=\mathrm{prewarp}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sysc2}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(s\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(s\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{s-2.}{as-s-2.a-2.}\end{array}\right.$

$\mathrm{sysd2}:=\mathrm{Resample}\left(\mathrm{sysd}\,2\,\mathrm{method}\=\mathrm{prewarp}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sysd2}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; 2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{z+3.}{az+3.z+3.a+1}\end{array}\right.$

$\mathrm{sys}:=\mathrm{TransferFunction}\left(\frac{1}{{\left(s\+1\right)}^2}\right)\:$

$\mathrm{NormH2}\left(\mathrm{sys}\right)$

$0.500000000000000$

$\mathrm{NormHinf}\left(\mathrm{sys}\right)$

$1.000001000$

$\mathrm{Covariance}\left(\mathrm{sys}\,⟨⟨1⟩⟩\right)$