TY - JOUR
T1 - Hybrid systems with state-triggered jumps
T2 - sensitivity-based stability analysis with application to trajectory tracking
AU - Rijnen, Mark
AU - Biemond, Benjamin
AU - van de Wouw, Nathan
AU - Saccon, Alessandro
AU - Nijmeijer, Henk
PY - 2020/11
Y1 - 2020/11
N2 - The definition of asymptotic stability for a trajectory of a hybrid system with state-triggered jumps is not straightforward. Nearby solutions jump at close but non-coincident times, making the standard notion of closeness, based on vector difference, unsuitable to compare trajectories point-wise in time. With tracking control as ultimate goal, we propose a notion of stability and a constructive stability proof based on sensitivity analysis applicable to single-jump-flow trajectories. A key role in the analysis is played by a time-triggered linear system, associated with the discontinuous trajectory of interest, whose uniform asymptotic stability suffices to guarantee the asymptotic stability of the original discontinuous trajectory. As an illustrative example, the stability analysis is applied to guarantee closed-loop stable tracking for a trajectory with velocity jumps of a 2 DoF mechanical system with unilateral constraint.
AB - The definition of asymptotic stability for a trajectory of a hybrid system with state-triggered jumps is not straightforward. Nearby solutions jump at close but non-coincident times, making the standard notion of closeness, based on vector difference, unsuitable to compare trajectories point-wise in time. With tracking control as ultimate goal, we propose a notion of stability and a constructive stability proof based on sensitivity analysis applicable to single-jump-flow trajectories. A key role in the analysis is played by a time-triggered linear system, associated with the discontinuous trajectory of interest, whose uniform asymptotic stability suffices to guarantee the asymptotic stability of the original discontinuous trajectory. As an illustrative example, the stability analysis is applied to guarantee closed-loop stable tracking for a trajectory with velocity jumps of a 2 DoF mechanical system with unilateral constraint.
KW - hybrid systems
KW - sensitivity analysis
KW - stability
KW - trajectories with jumps
KW - trajectory tracking
UR - http://www.scopus.com/inward/record.url?scp=85077272424&partnerID=8YFLogxK
U2 - 10.1109/TAC.2019.2961996
DO - 10.1109/TAC.2019.2961996
M3 - Article
AN - SCOPUS:85077272424
SN - 0018-9286
VL - 65
SP - 4568
EP - 4583
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
M1 - 8941288
ER -