TY - JOUR
T1 - Reachable set estimation for switched linear systems with dwell-time switching
AU - Baldi, Simone
AU - Xiang, Weiming
PY - 2018
Y1 - 2018
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://resolver.tudelft.nl/uuid:ab892cfd-eb6d-477f-a2eb-0a5e3c2cb738
UR - http://www.scopus.com/inward/record.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
SN - 1751-570X
VL - 29
SP - 20
EP - 33
JO - Nonlinear Analysis: Hybrid Systems
JF - Nonlinear Analysis: Hybrid Systems
ER -