Assign properties to \Delta-blocks

With the property ChannelClass you can associate a \Delta-block with the plant M as uncertainty, performance, or control channel.

Uncertainty channelSpecify if a \Delta-block is an uncertainty with:
– ChannelClass=’U’ (Default)
Performance channelSpecify if a \Delta-block is a performance channel with:
Control channelSpecify if a \Delta-block is an control channel with:

With the properties InputChannel and OutputChannel you can specify to which input- and output channels the \Delta-block is connected to M. There are three options as specified next.

Option 1For a single repeated SISO uncertainty block one should specify:

    \[\begin{array}{c} InputChannel=[C_x,\ldots,C_y]\\OutputChannel=[C_v,\ldots,C_w]\end{array}\]

with integers C_x, C_y, C_v, C_w.

Note: The order of the channels is not important.
Example 1For a scalar uncertainty that is repeated 3 times, and which is connected with the first 3 in- and output channels of M, one should specify:

    \[\begin{array}{c} InputChannel=[1:3]\\OutputChannel=[1:3]\end{array}\]

Option 2For a single repeated MIMO uncertainty block one should specify:

    \[\begin{array}{c} InputChannel=\left[\begin{array}{ccc}C_{\delta_{x_1}&\cdots&C_{\delta_{y_1}\\ \vdots&\vdots&\vdots\\ C_{\delta_{x_N}}&\cdots&C_{\delta_{y_N}}\end{array}\right]\\ OutputChannel=\left[\begin{array}{ccc}C_{\delta_{v_1}&\cdots&C_{\delta_{w_1}\\ \vdots&\vdots&\vdots\\ C_{\delta_{v_N}}&\cdots&C_{\delta_{w_N}}\end{array}\right]\]

where again the entries are integers.
Example 2For a full-block uncertainty of dimension 2\times3 that is repeated twice and which is respectively connected with the first 4 and 6 in- and output channels of M, one should specify:

    \[\begin{array}{c} InputChannel=[1,2;3,4]\\OutputChannel=[1:3;4:6]\end{array}\]

Option 3For multiple repeated SISO or MIMO uncertainty blocks one should proceed as before with the sole difference that each row should be specified as the element of a cell:

    \[\begin{array}{c} InputChannel=\{row_1,\ldots,row_N\},\\OutputChannel=\{row_1,\ldots,row_N \} .\end{array}\]

Example 3For two scalar uncertainties that are repeated 2 and 3 times respectively, and which are connected with the first 5 in- and outputs of M, one should specify

    \[\begin{array}{c} InputChannel=\{[1,2],[3:5]\}\\OutputChannel=\{[1,2],[3:5]\}\end{array}\]

Next to the previous properties, you can also specify the nature of the uncertainties via the following properties.

LinNonlinSpecify whether the uncertainty is linear (‘L’) or nonlinear (‘NL’). Default: ‘L’
TimInvTimeVarSpecify whether the uncertainty is time-invariant (‘TI’) or time-varying (‘TV’). Default: ‘TI’
StaticDynamicSpecify whether the uncertainty is static (‘S’) or dynamic (‘D’). Default: ‘S’
StructureSpecify whether the uncertainty is diagonal (‘D’) or full-block (‘FB’). Default: ‘D’

In addition, you can specify the characteristics of the uncertainties via the following properties.

BoundsSpecify (if any) the bounds on an uncertain parameter. For a single parameter and for multiple parameters respectively specify:
Bounds=[-b,b], b\geq0
Bounds=\{[-b_1,b_1],\ldots,[-b_N,b_N]\}, b_j\geq0
RateBoundsSpecify (if any) the rate bounds on an uncertain parameter. For a single parameter and for multiple parameters respectively specify:
RateBounds=[-b,b], b\geq0
RateBounds=\{[-b_1,b_1],\ldots,[-b_N,b_N]\}, b_j\geq0
NormBoundsSpecify (if any) the norm bound on an uncertainty/ nonlinearity:
NormBound=b, b\geq0
SectorBoundsSpecify (if any) the sector bounds on an uncertainty/ nonlinearity. For a single sector constraint and for multiple sector constraints respectively specify:
SectorBounds=[a,b], a\leq0\leq b
SectorBounds=\{[a_1,b_1],\ldots,[a_N,b_N]\}, a_j\leq0\leq b_j
SlopeBoundsSpecify (if any) the slope bounds on an uncertainty/ nonlinearity. For a single slope constraint and for multiple slope constraints respectively specify:
SlopeBounds=[a,b], a\leq0\leq b
SlopeBounds=\{[a_1,b_1],\ldots,[a_N,b_N]\}, a_j\leq0\leq b_j
PolytopeSpecify (if any) the generator points (i.e., the convex hull) of an uncertainty block:

    \[Polytope=\left[\begin{array}{ccc}\delta_1^{p_1}& \cdots& \delta_N^{p_1}\\ \vdots&\cdots&\vdots\\  \delta_1^{p_M}& \cdots& \delta_N^{p_M} \end{array}\right]\]

UncertaintyMapSpecify (if any) the uncertainty map of a parametric full-block uncertainty:

    \[\Delta(\delta)=\delta_1T_1+\cdots+ \delta_NT_N.\]

Here the matrices T_1,\ldots,T_N, which should all have the same dimension, must be specified as a cell array


DelayTime/ DelayTypeSpecify (if any) the maximum delay of the uncertain delay and the type of delay operator (see link for further details):
DelayTime=b, b\geq0
DelayType=c, c\in\{1,2\}
PassiveSpecify (if any) whether the uncertainty is passive:
– Passive=’Passive’
OddSpecify (if any) whether a nonlinearity is ‘Odd’:
– ‘yes’
– ‘no’ (default)
PerfMetricSpecify the performance metric. Respectively induced L_2-gain, H_2, generalized H_2, passive performance, and some invariance options as further specified here:

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