### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1998 |

### Publication series

Name | Memorandum / Department of Mathematics |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1475 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-90C33
- MSC-93A30
- EWI-3295
- IR-65664
- MSC-93B99

### Cite this

*Characterization of well-posedness of piecewise linear systems*. (Memorandum / Department of Mathematics; No. 1475). Enschede: University of Twente, Department of Applied Mathematics.

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*Characterization of well-posedness of piecewise linear systems*. Memorandum / Department of Mathematics, no. 1475, University of Twente, Department of Applied Mathematics, Enschede.

**Characterization of well-posedness of piecewise linear systems.** / Imura, J.I.; van der Schaft, Arjan.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Characterization of well-posedness of piecewise linear systems

AU - Imura, J.I.

AU - van der Schaft, Arjan

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed.

AB - One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed.

KW - MSC-90C33

KW - MSC-93A30

KW - EWI-3295

KW - IR-65664

KW - MSC-93B99

M3 - Report

T3 - Memorandum / Department of Mathematics

BT - Characterization of well-posedness of piecewise linear systems

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -