## Abstract

This technical note develops linear matrix inequality (LMI) conditions to test whether an uncertain linear system is exponentially stable with a given decay rate α. These new α- exponential stability tests are derived for an uncertain system described by an interconnection of a nominal linear time-invariant system and a 'troublesome' perturbation. The perturbation can contain uncertain parameters, time delays, or nonlinearities. This technical note presents two key contributions. First, α- exponential stability of the uncertain LTI system is shown to be equivalent to (internal) linear stability of a related scaled system. This enables derivation of α- exponential stability tests from linear stability tests using integral quadratic constraints (IQCs). This connection requires IQCs to be constructed for a scaled perturbation operator. The second contribution is a list of IQCs derived for the scaled perturbation using the detailed structure of the original perturbation. Finally, connections between the proposed approach and related work are discussed.

Original language | English (US) |
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Article number | 7393522 |

Pages (from-to) | 3631-3637 |

Number of pages | 7 |

Journal | IEEE Transactions on Automatic Control |

Volume | 61 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2016 |

### Bibliographical note

Publisher Copyright:© 1963-2012 IEEE.

## Keywords

- Exponential convergence rate
- integral quadratic constraint
- robustness