## Abstract

The challenging problem in linear control theory is to describe the total set of parameters (controller coefficients or plant characteristics) which provide stability of a system. For the case of one complex or two real parameters and SISO system (with a characteristic polynomial depending linearly on these parameters) the problem can be solved graphically by use of the so-called D-decomposition. Our goal is to extend the technique and to link it with general M-Δ framework. In this way we investigate the geometry of D-decomposition for polynomials and estimate the number of root invariant regions. Several examples verify that these estimates are tight. We also extend D-decomposition for the matrix case, i.e. for MIMO systems. For instance, we partition real axis or complex plane of the parameter k into regions with invariant number of stable eigenvalues of the matrix A+kB. Similar technique can be applied to double-input double-output systems with two parameters.

Original language | English |
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Pages (from-to) | 13-26 |

Number of pages | 14 |

Journal | Automatica |

Volume | 42 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2006 |

Externally published | Yes |

## Keywords

- Linear systems
- Parameter space
- Stability analysis
- Stability domain