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SystemsModelMerge[{sys1,sys2,…}]

merges the systems models sysj.

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SystemsModelMerge

SystemsModelMerge[{sys1,sys2,…}]

merges the systems models sysj.

Details

Examples

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Basic Examples  (4)

Merge two continuous-time systems:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{1}}, s*α}, s, SamplingPeriod -> None, SystemsModelLabels -> None], TransferFunctionModel[{{{b + s}}, a + s}, s, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Merge two discrete-time systems:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{b + z}}, a + z}, z, SamplingPeriod -> T, SystemsModelLabels -> None], TransferFunctionModel[{{{z + β}}, z + α}, z, SamplingPeriod -> T, SystemsModelLabels -> None]}]

Merge two StateSpaceModel systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{0, 1}, {-Subscript[α, 0], -Subscript[α, 1]}}, {{0}, {1}}, {{Subscript[β, 0], Subscript[β, 1]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{0, 1}, {-Subscript[a, 0], -Subscript[a, 1]}}, {{0}, {1}}, {{Subscript[b, 0], Subscript[b, 1]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Merge AffineStateSpaceModel systems with a common input variable:

Wolfram Language code: SystemsModelMerge[{AffineStateSpaceModel[{{-a Subscript[x, 1]}, {{b}}, {Subscript[x, 1]}, {{0}}}, {Subscript[x, 1]}, {Subscript[u, 1]}], AffineStateSpaceModel[{{α Subsuperscript[x, 2, 2]}, {{β}}, {Subscript[x, 2]}, {{0}}}, {Subscript[x, 2]}, {Subscript[u, 1]}]}]

Scope  (13)

Basic Uses  (5)

Merge two scalar systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11]}, {Subscript[b, 21]}}, {{Subscript[c, 11], Subscript[c, 12]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{Subscript[α, 11], Subscript[α, 12]}, {Subscript[α, 21], Subscript[α, 22]}}, {{Subscript[β, 11]}, {Subscript[β, 21]}}, {{Subscript[γ, 11], Subscript[γ, 12]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Merge three systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11], Subscript[b, 12]}, {Subscript[b, 21], Subscript[b, 22]}}, {{Subscript[c, 11], Subscript[c, 12]}, {Subscript[c, 21], Subscript[c, 22]}}, {{Subscript[d, 11], Subscript[d, 12]}, {Subscript[d, 21], Subscript[d, 22]}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{Subscript[α, 11], Subscript[α, 12]}, {Subscript[α, 21], Subscript[α, 22]}}, {{Subscript[β, 11], Subscript[β, 12]}, {Subscript[β, 21], Subscript[β, 22]}}, {{Subscript[γ, 11], Subscript[γ, 12]}}, {{Subscript[D, 11], Subscript[D, 12]}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{Α}}, {{Β}}, {{Χ}}, {{Δ}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Merge systems that share input variables:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11]}, {Subscript[b, 21]}}, {{Subscript[c, 11], Subscript[c, 12]}, {Subscript[c, 21], Subscript[c, 22]}}, {{0}, {0}}}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[u, 1]}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{Subscript[α, 11], Subscript[α, 12]}, {Subscript[α, 21], Subscript[α, 22]}}, {{Subscript[β, 11], Subscript[β, 12]}, {Subscript[β, 21], Subscript[β, 22]}}, {{Subscript[γ, 11], Subscript[γ, 12]}}, {{0, 0}}}, {Subscript[ξ, 1], Subscript[ξ, 2]}, {Subscript[u, 1], Subscript[u, 2]}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

When an input and state have the same variable name, the state defines the input:

Wolfram Language code: Subscript[ssm, 1] = StateSpaceModel[{(⁠| | | | --- | --- | | a11 | a12 | | a21 | a22 |⁠), (⁠| | | --- | | b11 | | b21 |⁠), (⁠| | | | --- | --- | | c11 | c12 | | c21 | c22 |⁠), (⁠| | | - | | 0 | | 0 |⁠)}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[u, 1]}];
Wolfram Language code: Subscript[ssm, 2] = StateSpaceModel[{(⁠| | | | --- | --- | | α11 | α12 | | α21 | α22 |⁠), (⁠| | | | --- | --- | | β11 | β12 | | β21 | β22 |⁠), (⁠Subscript[γ, 11] Subscript[γ, 12]⁠), (⁠0 0⁠)}, {Subscript[ξ, 1], Subscript[ξ, 2]}, {Subscript[x, 1], Subscript[u, 2]}];
Wolfram Language code: SystemsModelMerge[{Subscript[ssm, 1], Subscript[ssm, 2]}]

Merge a StateSpaceModel and a TransferFunctionModel:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11]}, {Subscript[b, 21]}}, {{Subscript[c, 11], Subscript[c, 12]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], TransferFunctionModel[{{{k}}, s + α}, s]}]

System Types  (8)

Merge two TransferFunctionModel systems:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{a}}, p + s}, s, SamplingPeriod -> None, SystemsModelLabels -> None], TransferFunctionModel[{{{α}}, s + ρ}, s]}]

Delay systems:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{a/E^(s*T)}}, p + s}, s], TransferFunctionModel[{{{α/E^(s*τ)}}, s + ρ}, s]}]

Improper transfer functions:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{a + s}}, 1}, s, SamplingPeriod -> None, SystemsModelLabels -> None], TransferFunctionModel[{{{s + α}}, 1}, s, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Merge two StateSpaceModel systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α}}, {{β}}, {{γ}}, {{ρ}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Delay systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{a + SystemsModelDelay[Subscript[τ, 1]]}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α + SystemsModelDelay[Subscript[τ, 2]]}}, {{β}}, {{γ}}, {{ρ}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Descriptor state-space systems:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}, {{e}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α}}, {{β}}, {{γ}}, {{ρ}}, {{η}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

AffineStateSpaceModel systems:

Wolfram Language code: SystemsModelMerge[{AffineStateSpaceModel[{{a[Subscript[x, 1]]}, {{b[Subscript[x, 1]]}}, {c[Subscript[x, 1]]}, {{d[Subscript[x, 1]]}}}, {Subscript[x, 1]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], AffineStateSpaceModel[{{α[Subscript[x, 2]]}, {{β[Subscript[x, 2]]}}, {γ[Subscript[x, 2]]}, {{ρ[Subscript[x, 2]]}}}, {Subscript[x, 2]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None]}]

NonlinearStateSpaceModel systems:

Wolfram Language code: SystemsModelMerge[{NonlinearStateSpaceModel[{{Subscript[f, 1][Subscript[x, 1], Subscript[u, 1]]}, {Subscript[h, 1][Subscript[x, 1], Subscript[u, 1]]}}, {Subscript[x, 1]}, {Subscript[u, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], NonlinearStateSpaceModel[{{Subscript[f, 2][Subscript[x, 2], Subscript[u, 2]]}, {Subscript[h, 2][Subscript[x, 2], Subscript[u, 2]]}}, {Subscript[x, 2]}, {Subscript[u, 2]}, {Automatic}, Automatic, SamplingPeriod -> None]}]

Merging a TransferFunctionModel and StateSpaceModel will give a StateSpaceModel:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{k*(s + Subscript[z, 1])}}, s + Subscript[p, 1]}, s, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Systems with delays:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{k*(s + Subscript[z, 1])}}, E^(s*Subscript[τ, 1])*(s + Subscript[p, 1])}, s, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{a + SystemsModelDelay[Subscript[τ, 2]]}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None]}]

Standard linear system and an AffineStateSpaceModel will give an AffineStateSpaceModel:

Wolfram Language code: SystemsModelMerge[{TransferFunctionModel[{{{k*(s + Subscript[z, 1])}}, s + Subscript[p, 1]}, s, SamplingPeriod -> None, SystemsModelLabels -> None], AffineStateSpaceModel[{{α[x]}, {{β[x]}}, {γ[x]}, {{ρ[x]}}}, {x}, {Subscript[u, 1]}, {Automatic}, Automatic, SamplingPeriod -> None]}]
Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], AffineStateSpaceModel[{{α[x]}, {{β[x]}}, {γ[x]}, {{ρ[x]}}}, {x}, {Subscript[u, 1]}, {Automatic}, Automatic, SamplingPeriod -> None]}]

Standard linear with NonlinearStateSpaceModel gives a NonlinearStateSpaceModel:

Wolfram Language code: SystemsModelMerge[{StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], NonlinearStateSpaceModel[{{f[x, u]}, {h[x, u]}}, {x}, {u}, {Automatic}, Automatic, SamplingPeriod -> None]}]

AffineStateSpaceModel with NonlinearStateSpaceModel again gives the latter:

Wolfram Language code: SystemsModelMerge[{AffineStateSpaceModel[{{a[Subscript[x, 1]]}, {{b[Subscript[x, 1]]}}, {c[Subscript[x, 1]]}, {{d[Subscript[x, 1]]}}}, {Subscript[x, 1]}, {Subscript[u, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], NonlinearStateSpaceModel[{{f[Subscript[x, 2], Subscript[u, 2]]}, {h[Subscript[x, 2], Subscript[u, 2]]}}, {Subscript[x, 2]}, {Subscript[u, 2]}, {Automatic}, Automatic, SamplingPeriod -> None]}]

Applications  (1)

Use SystemsModelMerge in multi-loop reduction:

The subsystems:

Wolfram Language code: {Subscript[sys, 1], Subscript[sys, 2], Subscript[sys, 3], Subscript[sys, 4]} = {TransferFunctionModel[{{{1}}, 10 + s}, s], TransferFunctionModel[{{{1}}, 1 + s}, s], TransferFunctionModel[{{{1 + s^2}}, 4 + 4*s + s^2}, s], TransferFunctionModel[{{{1 + s}}, 6 + s}, s]};
Wolfram Language code: {Subscript[fsys, 1], Subscript[fsys, 2], Subscript[fsys, 3]} = {TransferFunctionModel[{{{1 + s}}, 2 + s}, s], TransferFunctionModel[{{{2*(6 + s)}}, 1 + s}, s], TransferFunctionModel[{{{1}}, 1}, s]};
Wolfram Language code: Subscript[sum, 1] = Subscript[sum, 2] = TransferFunctionModel[{{{1, -1}}, 1}, s];
Wolfram Language code: Subscript[sum, 3] = TransferFunctionModel[{{{1, 1}}, 1}, s];
Wolfram Language code: asys = {Subscript[sys, 1], Subscript[sys, 2], Subscript[sys, 3], Subscript[sys, 4], Subscript[fsys, 1], Subscript[fsys, 2], Subscript[fsys, 3], Subscript[sum, 1], Subscript[sum, 2], Subscript[sum, 3]};

The connections:

Wolfram Language code: conxs = {{8, 1} -> {1, 1}, {1, 1} -> {9, 1}, {9, 1} -> {2, 1}, {2, 1} -> {10, 1}, {10, 1} -> {3, 1}, {3, 1} -> {4, 1}, {4, 1} -> {6, 1}, {6, 1} -> {9, 2}, {4, 1} -> {5, 1}, {5, 1} -> {10, 2}, {4, 1} -> {7, 1}, {7, 1} -> {8, 2}};

The inputs and outputs:

Wolfram Language code: ins = {{8, 1}}; outs = {{4, 1}};

The connections model:

Wolfram Language code: SystemsConnectionsModel[asys, conxs, ins, outs]

Reduce the system:

Wolfram Language code: SystemsModelMerge[%]

Properties & Relations  (4)

By default, SystemsModelMerge does not connect inputs or sum outputs:

Wolfram Language code: {Subscript[tfm, 1], Subscript[tfm, 2]} = Table[TransferFunctionModel[{{{1}}, s + Subscript[α, i]}, s], {i, 2}];
Wolfram Language code: SystemsModelMerge[{Subscript[tfm, 1], Subscript[tfm, 2]}]

SystemsModelParallelConnect connects inputs and sums outputs:

Wolfram Language code: SystemsModelParallelConnect[Subscript[tfm, 1], Subscript[tfm, 2]]

When no variables match, SystemsModelMerge is a case of SystemsModelParallelConnect:

Wolfram Language code: {Subscript[tfm, 1], Subscript[tfm, 2]} = Table[TransferFunctionModel[{{{1}}, s + Subscript[α, i]}, s], {i, 2}];
Wolfram Language code: {SystemsModelMerge[{Subscript[tfm, 1], Subscript[tfm, 2]}], SystemsModelParallelConnect[Subscript[tfm, 1], Subscript[tfm, 2], None, None]}

SystemsModelMerge can be used to merge two or more systems:

Wolfram Language code: {Subscript[tfm, 1], Subscript[tfm, 2], Subscript[tfm, 3]} = Table[TransferFunctionModel[{{{1}}, s + Subscript[α, i]}, s], {i, 3}];
Wolfram Language code: SystemsModelMerge[{Subscript[tfm, 1], Subscript[tfm, 2], Subscript[tfm, 3]}]

SystemsModelParallelConnect connects only two systems:

Wolfram Language code: SystemsModelParallelConnect[Subscript[tfm, 1], Subscript[tfm, 2], None, None]

SystemsModelMerge can merge a system with no inputs or outputs to another system:

Wolfram Language code: Subscript[asys, 1] = AffineStateSpaceModel[{{Subscript[x, 2]}, {}, {}}, {Subscript[x, 1]}];
Wolfram Language code: Subscript[asys, 2] = AffineStateSpaceModel[{{Subscript[x, 1]}, {{1}}, {Subscript[x, 2]}}, {Subscript[x, 2]}, {u}];
Wolfram Language code: SystemsModelMerge[{Subscript[asys, 1], Subscript[asys, 2]}]

It does not make sense to connect such systems in parallel:

Wolfram Language code: SystemsModelParallelConnect[Subscript[asys, 1], Subscript[asys, 2]]
Wolfram Research (2014), SystemsModelMerge, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelMerge.html.

Text

Wolfram Research (2014), SystemsModelMerge, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelMerge.html.

CMS

Wolfram Language. 2014. "SystemsModelMerge." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SystemsModelMerge.html.

APA

Wolfram Language. (2014). SystemsModelMerge. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemsModelMerge.html

BibTeX

@misc{reference.wolfram_2026_systemsmodelmerge, author="Wolfram Research", title="{SystemsModelMerge}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelMerge.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_systemsmodelmerge, organization={Wolfram Research}, title={SystemsModelMerge}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelMerge.html}, note=[Accessed: 13-June-2026]}