### Abstract

squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on

the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed

through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide

range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank

reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

Original language | English |
---|---|

Journal | Transactions of the Institute of Measurement and Control |

Volume | 41 |

Issue number | 7 |

Number of pages | 12 |

ISSN | 0142-3312 |

DOIs | |

Publication status | Published - 2019 |

### Fingerprint

### Keywords

- Polynomial chaotic system
- Polynomial CSTR plant
- Polynomial PMSM system
- Sum of squares (SOS) decomposistion
- Polynomial Lyapunov function
- Software-in-the-loop (SiL)

### Cite this

*Transactions of the Institute of Measurement and Control*,

*41*(7). https://doi.org/10.1177/0142331218793476

}

*Transactions of the Institute of Measurement and Control*, vol. 41, no. 7. https://doi.org/10.1177/0142331218793476

**Polynomial control design for polynomial systems: A non-iterative sum of squares approach.** / Rakhshan, Mohsen; Vafamand, Navid; Mardani, Mohammad Mehdi; Khooban, Mohammad Hassan; Dragicevic, Tomislav.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Polynomial control design for polynomial systems: A non-iterative sum of squares approach

AU - Rakhshan, Mohsen

AU - Vafamand, Navid

AU - Mardani, Mohammad Mehdi

AU - Khooban, Mohammad Hassan

AU - Dragicevic, Tomislav

PY - 2019

Y1 - 2019

N2 - This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum ofsquares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound onthe time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computedthrough semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a widerange of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tankreactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

AB - This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum ofsquares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound onthe time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computedthrough semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a widerange of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tankreactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

KW - Polynomial chaotic system

KW - Polynomial CSTR plant

KW - Polynomial PMSM system

KW - Sum of squares (SOS) decomposistion

KW - Polynomial Lyapunov function

KW - Software-in-the-loop (SiL)

U2 - 10.1177/0142331218793476

DO - 10.1177/0142331218793476

M3 - Journal article

VL - 41

JO - Transactions of the Institute of Measurement and Control

JF - Transactions of the Institute of Measurement and Control

SN - 0142-3312

IS - 7

ER -