## Abstract

We study the global asymptotic stability in probability of the zero solution of linear stochastic differential equations with constant coefficients. We develop a sum-of-squares program that verifies whether a parameterized candidate Lyapunov function is in fact a global Lyapunov function for such a system. Our class of candidate Lyapunov functions are naturally adapted to the problem. We consider functions of the form V (x) = ||x||^{p}_{Q} := (x^{τ}Qx)^{p/2}, where the parameters are the positive definite matrix Q and the number p > 0. We give several examples of our proposed method and show how it improves previous results.

Original language | English |
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Pages (from-to) | 939-956 |

Number of pages | 18 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 23 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2018 |

## Other keywords

- Basin of attraction
- Dynamical system
- Lyapunov function
- Numerical method
- Stability
- Stochastic differential equation