## Abstract

In the design of decentralized networked systems, it is important to know whether a given network topology can sustain stable dynamics. We consider a basic version of this problem here: given a vector space of sparse real matrices, does it contain a stable (Hurwitz) matrix? Said differently, is a feedback channel (corresponding to a non-zero entry) necessary for stabilization or can it be done without? We provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices. We further prove some properties of the set of sparse matrix spaces that contain Hurwitz matrices. The conditions we exhibit are most easily stated in the language of graph theory, which we thus adopt in this paper.

Original language | English (US) |
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Pages (from-to) | 981-987 |

Number of pages | 7 |

Journal | Systems and Control Letters |

Volume | 62 |

Issue number | 10 |

DOIs | |

State | Published - Sep 3 2013 |

## Keywords

- Decentralized control
- Graph theory
- Hamiltonian cycles
- Network control
- Stability

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering