### Abstract

A robust synthesis algorithm is developed for a class of uncertain, linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured uncertainty. The nominal part is a "gridded" LPV system with state matrices that are arbitrary functions of the parameter. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). The robust synthesis problem leads to a non-convex optimization. The proposed algorithm is a coordinate-wise descent similar to the well-known DK iteration for μ synthesis. It alternates between an LPV synthesis step and an IQC analysis step. Both steps can be efficiently solved as semidefinite programs. The derivation of the synthesis algorithm is less obvious for LPV systems as compared to its LTI counterpart due to the lack of a valid frequency response interpretation. The main contribution is the construction of the iterative synthesis algorithm using time domain dissipation inequalities and a scaled system analogous to that appearing in μ synthesis. It is shown that the proposed algorithm ensures that the robust performance is non-increasing at each iteration step. The effectiveness of the proposed method is demonstrated on a simple numerical example.

Original language | English (US) |
---|---|

Pages (from-to) | 111-118 |

Number of pages | 8 |

Journal | Automatica |

Volume | 68 |

DOIs | |

State | Published - Jan 1 2016 |

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### Keywords

- Integral quadratic constraints
- Linear parameter varying systems
- Robust control
- Semidefinite programs

### Cite this

*Automatica*,

*68*, 111-118. https://doi.org/10.1016/j.automatica.2016.01.053

**Robust synthesis for linear parameter varying systems using integral quadratic constraints.** / Wang, Shu; Pfifer, Harald; Seiler Jr, Peter J.

Research output: Contribution to journal › Article

*Automatica*, vol. 68, pp. 111-118. https://doi.org/10.1016/j.automatica.2016.01.053

}

TY - JOUR

T1 - Robust synthesis for linear parameter varying systems using integral quadratic constraints

AU - Wang, Shu

AU - Pfifer, Harald

AU - Seiler Jr, Peter J

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A robust synthesis algorithm is developed for a class of uncertain, linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured uncertainty. The nominal part is a "gridded" LPV system with state matrices that are arbitrary functions of the parameter. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). The robust synthesis problem leads to a non-convex optimization. The proposed algorithm is a coordinate-wise descent similar to the well-known DK iteration for μ synthesis. It alternates between an LPV synthesis step and an IQC analysis step. Both steps can be efficiently solved as semidefinite programs. The derivation of the synthesis algorithm is less obvious for LPV systems as compared to its LTI counterpart due to the lack of a valid frequency response interpretation. The main contribution is the construction of the iterative synthesis algorithm using time domain dissipation inequalities and a scaled system analogous to that appearing in μ synthesis. It is shown that the proposed algorithm ensures that the robust performance is non-increasing at each iteration step. The effectiveness of the proposed method is demonstrated on a simple numerical example.

AB - A robust synthesis algorithm is developed for a class of uncertain, linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured uncertainty. The nominal part is a "gridded" LPV system with state matrices that are arbitrary functions of the parameter. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). The robust synthesis problem leads to a non-convex optimization. The proposed algorithm is a coordinate-wise descent similar to the well-known DK iteration for μ synthesis. It alternates between an LPV synthesis step and an IQC analysis step. Both steps can be efficiently solved as semidefinite programs. The derivation of the synthesis algorithm is less obvious for LPV systems as compared to its LTI counterpart due to the lack of a valid frequency response interpretation. The main contribution is the construction of the iterative synthesis algorithm using time domain dissipation inequalities and a scaled system analogous to that appearing in μ synthesis. It is shown that the proposed algorithm ensures that the robust performance is non-increasing at each iteration step. The effectiveness of the proposed method is demonstrated on a simple numerical example.

KW - Integral quadratic constraints

KW - Linear parameter varying systems

KW - Robust control

KW - Semidefinite programs

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U2 - 10.1016/j.automatica.2016.01.053

DO - 10.1016/j.automatica.2016.01.053

M3 - Article

VL - 68

SP - 111

EP - 118

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -