### Abstract

In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase at switching times), we overcome the need for such properties. This is done by introducing a new notion of τ-reachable set, i.e. the set that can be reached by the trajectories defined at time τ after the switch. Such extended notion of reachable set can be used to parametrize the estimate of the reachable set as a function of the distance in time from the switch. Two approaches are provided to implement such parametrization: the first approach exploits the evolution of the system in between switches via the matrix exponential of the state subsystem matrix; the second approach exploits a time-scheduled Lyapunov function. A numerical example is provided to show the effectiveness of the proposed methods and computational cost is addressed.

Original language | English (US) |
---|---|

Pages (from-to) | 20-33 |

Number of pages | 14 |

Journal | Nonlinear Analysis: Hybrid Systems |

Volume | 29 |

DOIs | |

State | Published - Aug 1 2018 |

### Fingerprint

### Keywords

- Dwell-time switching
- Reachable set estimation
- Switched linear systems

### ASJC Scopus subject areas

- Control and Systems Engineering
- Analysis
- Computer Science Applications

### Cite this

*Nonlinear Analysis: Hybrid Systems*,

*29*, 20-33. https://doi.org/10.1016/j.nahs.2017.12.004

**Reachable set estimation for switched linear systems with dwell-time switching.** / Baldi, Simone; Xiang, Weiming.

Research output: Contribution to journal › Article

*Nonlinear Analysis: Hybrid Systems*, vol. 29, pp. 20-33. https://doi.org/10.1016/j.nahs.2017.12.004

}

TY - JOUR

T1 - Reachable set estimation for switched linear systems with dwell-time switching

AU - Baldi, Simone

AU - Xiang, Weiming

PY - 2018/8/1

Y1 - 2018/8/1

N2 - In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase at switching times), we overcome the need for such properties. This is done by introducing a new notion of τ-reachable set, i.e. the set that can be reached by the trajectories defined at time τ after the switch. Such extended notion of reachable set can be used to parametrize the estimate of the reachable set as a function of the distance in time from the switch. Two approaches are provided to implement such parametrization: the first approach exploits the evolution of the system in between switches via the matrix exponential of the state subsystem matrix; the second approach exploits a time-scheduled Lyapunov function. A numerical example is provided to show the effectiveness of the proposed methods and computational cost is addressed.

AB - In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase at switching times), we overcome the need for such properties. This is done by introducing a new notion of τ-reachable set, i.e. the set that can be reached by the trajectories defined at time τ after the switch. Such extended notion of reachable set can be used to parametrize the estimate of the reachable set as a function of the distance in time from the switch. Two approaches are provided to implement such parametrization: the first approach exploits the evolution of the system in between switches via the matrix exponential of the state subsystem matrix; the second approach exploits a time-scheduled Lyapunov function. A numerical example is provided to show the effectiveness of the proposed methods and computational cost is addressed.

KW - Dwell-time switching

KW - Reachable set estimation

KW - Switched linear systems

UR - http://www.scopus.com/inward/record.url?scp=85043291078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043291078&partnerID=8YFLogxK

U2 - 10.1016/j.nahs.2017.12.004

DO - 10.1016/j.nahs.2017.12.004

M3 - Article

AN - SCOPUS:85043291078

VL - 29

SP - 20

EP - 33

JO - Nonlinear Analysis: Hybrid Systems

JF - Nonlinear Analysis: Hybrid Systems

SN - 1751-570X

ER -