TY - JOUR
T1 - Approximating the Steady-State Periodic Solutions of Contractive Systems
AU - Coogan, Samuel
AU - Margaliot, Michael
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/2
Y1 - 2019/2
N2 - We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic, then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications. We develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system (e.g., an LTI system). The approximation includes an error bound that is based on the input-to-state stability property of contractive systems. We show that in some cases, this error bound can be computed explicitly. We also use the bound to derive a new theoretical result, namely, that a contractive system with an additive periodic input behaves like a low-pass filter. We demonstrate our results using several examples from systems biology.
AB - We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic, then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications. We develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system (e.g., an LTI system). The approximation includes an error bound that is based on the input-to-state stability property of contractive systems. We show that in some cases, this error bound can be computed explicitly. We also use the bound to derive a new theoretical result, namely, that a contractive system with an additive periodic input behaves like a low-pass filter. We demonstrate our results using several examples from systems biology.
KW - Computational methods
KW - entrainment
KW - stability of nonlinear systems
KW - systems biology
UR - http://www.scopus.com/inward/record.url?scp=85047085661&partnerID=8YFLogxK
U2 - 10.1109/TAC.2018.2838054
DO - 10.1109/TAC.2018.2838054
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85047085661
SN - 0018-9286
VL - 64
SP - 847
EP - 853
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 2
M1 - 8360452
ER -