The class *usbsr* is defined by diagonally repeated sector-bounded and slope-restricted nonlinearities of the form

Here

- The sector constraint for all and fixed constants
- and optionally, the incremental sector constraint (slope restriction)

*Note:*

*. Hence, if desired, one can consider tighter sector bounds with and .**For mathematically more precise formulations of the constraints see [1] and respectively [2] and [23] for the continuous- and discrete time version respectively.*

The *usbsr* class can be defined by

Just specifying defines a sector bounded nonlinearity, which is repeated once, and which satisfies the constraint .

Specifying and/or changing properties proceeds as summarized in the following two tables for properties related to the uncertainty and to IQC-multiplier respectively.

Property | Description |

NumberOfRepetitions | Specify the number of repetitions of the nonlinearity (default = 1). |

SectorBounds | Specify the sector constraints , (default = [0,1]). |

SlopeBounds | Specify the slope bounds , (default = [0,0]). |

Odd | Specify whether the nonlinearity is Odd (i.e., ):– ‘ yes‘– (default)‘no‘ |

InputChannel/ OutputChannel | Specify which input and output channels of the uncertain plant are affected by . The channels should be specified as:
Here the order of the channels is not relevant, while , respectively denote the and in- and output channel of the uncertain plant . |

Property | Description |

BasisFunctionType | Specify the type of basis function to be used in the multiplier (default = 1). See link for further details. |

Length | Specify the length of the basis function (default = 1). See link for further details. |

PoleLocation | Specify the pole location of the basis function (default = -1). See link for further details. |

SampleTime | Specify the sample time (default = 0). |

PrimalDual | Specify whether the multiplier should be a primal/dual parametrization (default = ‘Primal’).– Primal multipliers: ‘Primal’ – Dual multipliers: ‘Dual’ Note: For a standard IQC-analysis, all multipliers must be primal ones. |