TY - GEN
T1 - A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems
AU - Murti, Chaitanya
AU - Peet, Matthew
PY - 2013
Y1 - 2013
N2 - Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.
AB - Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.
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U2 - 10.23919/ecc.2013.6669823
DO - 10.23919/ecc.2013.6669823
M3 - Conference contribution
AN - SCOPUS:84893268508
SN - 9783033039629
T3 - 2013 European Control Conference, ECC 2013
SP - 1657
EP - 1662
BT - 2013 European Control Conference, ECC 2013
PB - IEEE Computer Society
T2 - 2013 12th European Control Conference, ECC 2013
Y2 - 17 July 2013 through 19 July 2013
ER -