### Abstract

The uniform stability of discrete-time switched linear systems, possibly with a strongly connected switching path constraint, and the existence of finite-path-dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite-dimensional feasible system of linear matrix inequalities. This characterization is based on the observation that a linear time-varying system is uniformly stable only if there exists a finite-path-dependent quadratic Lyapunov function. The synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities. The result carries over to the almost sure uniform stabilization of Markovian jump linear systems.

Original language | English (US) |
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Pages (from-to) | 205-218 |

Number of pages | 14 |

Journal | Automatica |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2006 |

### Keywords

- Discrete linear inclusions
- Dynamic output feedback
- Linear matrix inequalities
- Linear time-varying systems
- Uniform exponential stability

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering