### Abstract

The aim of this paper is to investigate a geometric theory for a class of dynamical systems called Linear Parameter Varying (LPV) systems. A wide class of nonlinear systems can be presented in LPV form and this makes the use of many linear analysis and design methods possible for these nonlinear systems. This paper extends the concept of (A,B)-invariant and (C,A)-invariant subspaces known in the geometric control theory of for linear time invariant (LTI) systems to the LPV systems by introducing the concept of parameter-varying (A,B)-invariant and parameter-varying (C,A)-invariant subspaces. The parameter dependence in the state matrix of these LPV systems is assumed to be in affine form. Algorithms are given to compute these subepaces and it is shown how these subspaces are related to certain invariant distributions if certain conditions are fulfilled for the parameters. As an application a condition is given for the solvability of disturbance decoupling problem and for the solvability of the fundamental problem of residual generation problem for LPV systems.

Original language | English |
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Pages | 13-20 |

Number of pages | 8 |

Publication status | Published - Dec 1 2002 |

Event | 8th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2002 - Budapest, Hungary Duration: Nov 11 2002 → Nov 13 2002 |

### Other

Other | 8th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2002 |
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Country | Hungary |

City | Budapest |

Period | 11/11/02 → 11/13/02 |

### Keywords

- Controllability
- Invariant subspaces
- LPV systems
- Nonlinear systems
- Observability

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*A geometric theory of linear parameter varying systems*. 13-20. Paper presented at 8th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2002, Budapest, Hungary.