### Abstract

In this paper, we propose a parallel algorithm to solve the problem of robust stability of systems with large state-space and with large number of uncertain parameters. The dependence of the system on the parameters is polynomial and the parameters are assumed to lie in a hypercube. Although the parameters are assumed to be static, the method can also be applied to systems with time-varying parameters. The algorithm relies on a variant of Polya's theorem which is applicable to polynomials with variables inside a multi-simplex. The algorithm is divided into formulation and solution subroutines. In the formulation phase, we construct a large-scale semidefinite programming problem with structured elements. In the solution phase, we use a structured primal-dual approach to solve the structured semidefinite programming problem. In both subroutines, computation, memory and communication are efficiently distributed over hundreds and potentially thousands of processors. Numerical tests confirm the accuracy and scalability of the proposed algorithm.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 6259-6264 |

Number of pages | 6 |

DOIs | |

State | Published - 2012 |

Event | 51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: Dec 10 2012 → Dec 13 2012 |

### Other

Other | 51st IEEE Conference on Decision and Control, CDC 2012 |
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Country | United States |

City | Maui, HI |

Period | 12/10/12 → 12/13/12 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 6259-6264). [6425907] https://doi.org/10.1109/CDC.2012.6425907

**Decentralized computation for robust stability of large-scale systems with parameters on the hypercube.** / Kamyar, Reza; Peet, Matthew M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*, 6425907, pp. 6259-6264, 51st IEEE Conference on Decision and Control, CDC 2012, Maui, HI, United States, 12/10/12. https://doi.org/10.1109/CDC.2012.6425907

}

TY - GEN

T1 - Decentralized computation for robust stability of large-scale systems with parameters on the hypercube

AU - Kamyar, Reza

AU - Peet, Matthew M.

PY - 2012

Y1 - 2012

N2 - In this paper, we propose a parallel algorithm to solve the problem of robust stability of systems with large state-space and with large number of uncertain parameters. The dependence of the system on the parameters is polynomial and the parameters are assumed to lie in a hypercube. Although the parameters are assumed to be static, the method can also be applied to systems with time-varying parameters. The algorithm relies on a variant of Polya's theorem which is applicable to polynomials with variables inside a multi-simplex. The algorithm is divided into formulation and solution subroutines. In the formulation phase, we construct a large-scale semidefinite programming problem with structured elements. In the solution phase, we use a structured primal-dual approach to solve the structured semidefinite programming problem. In both subroutines, computation, memory and communication are efficiently distributed over hundreds and potentially thousands of processors. Numerical tests confirm the accuracy and scalability of the proposed algorithm.

AB - In this paper, we propose a parallel algorithm to solve the problem of robust stability of systems with large state-space and with large number of uncertain parameters. The dependence of the system on the parameters is polynomial and the parameters are assumed to lie in a hypercube. Although the parameters are assumed to be static, the method can also be applied to systems with time-varying parameters. The algorithm relies on a variant of Polya's theorem which is applicable to polynomials with variables inside a multi-simplex. The algorithm is divided into formulation and solution subroutines. In the formulation phase, we construct a large-scale semidefinite programming problem with structured elements. In the solution phase, we use a structured primal-dual approach to solve the structured semidefinite programming problem. In both subroutines, computation, memory and communication are efficiently distributed over hundreds and potentially thousands of processors. Numerical tests confirm the accuracy and scalability of the proposed algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84874287048&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874287048&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6425907

DO - 10.1109/CDC.2012.6425907

M3 - Conference contribution

SP - 6259

EP - 6264

BT - Proceedings of the IEEE Conference on Decision and Control

ER -