# Discretization of Linear Fractional Representations of LPV systems

TL;DR: The proposed and existing methods are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling, and criteria to choose appropriate sampling times with respect to the investigated methods are presented.

Abstract: Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing discretization approaches for LFRs suffer from disadvantages like alternation of dynamics, complexity, etc. To overcome the disadvantages, novel discretization methods are derived. These approaches are compared to existing techniques and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling.

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### Cites background from "Discretization of Linear Fractional..."

...Unfortunately, transformation of DT-LPV models to CT-LPV mo dels is more complicated than in the LTI case and despite recent advances in LPV discretiza tion theory (see [13], [14]) the theory of CT realization of DT models is still in an immature st ate....

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### Cites background from "Discretization of Linear Fractional..."

...It is well known that there is a correspondence between LPVs and LFT representations [19], [17]....

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##### References

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30,199 citations

### "Discretization of Linear Fractional..." refers methods in this paper

...Full zero-order hold approaches A commonly used approach, like in [4], [5], is to apply ZOHs and sampling on all signals of (1a-b) (see Figure 1b)....

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...Basically the available methods use Zero-Order Hold (ZOH) and First-Order Hold (1OH) approaches to restrict the variations of the signals of the LFR in the sample interval which results in a DT description of the dynamics [4], [5], [6], [7], [8], [9], [10], [11]....

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6,941 citations

### "Discretization of Linear Fractional..." refers background in this paper

..., [3])...

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...The main reason is that stability and performance requirements can be more conveniently expressed in CT, like in a mixed sensitivity setting [3]....

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..., [1]–[3]), often require LPV models in a linear fractional representation (LFR), as depicted in Fig....

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4,051 citations

### "Discretization of Linear Fractional..." refers methods in this paper

...In Section VI a numerical example is given for the comparison of the approaches....

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4,038 citations