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

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

Baldi, S. (TU Delft Team Bart De Schutter)
Xiang, Weiming (VanderBilt University; Southwest Jiaotong University)

2018

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.

Dwell-time switching
Reachable set estimation
Switched linear systems

http://resolver.tudelft.nl/uuid:ab892cfd-eb6d-477f-a2eb-0a5e3c2cb738

https://doi.org/10.1016/j.nahs.2017.12.004

2020-01-31

1751-570X

Nonlinear Analysis: Hybrid Systems, 29, 20-33

Institutional Repository

journal article

© 2018 S. Baldi, Weiming Xiang