### Abstract

This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

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

Title of host publication | Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC |

Pages | 1722-1727 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2007 |

Event | 46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|

ISSN (Print) | 0191-2216 |

### Other

Other | 46th IEEE Conference on Decision and Control 2007, CDC |
---|---|

Country | United States |

City | New Orleans, LA |

Period | 12/12/07 → 12/14/07 |

### All Science Journal Classification (ASJC) codes

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

## Fingerprint Dive into the research topics of 'Nonlinear stabilization via control-Lyapunov measure'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC*(pp. 1722-1727). [4434956] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434956