TY - GEN
T1 - Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Implicit Systems
AU - Immanuel, Gidado Yisa
AU - Abate, Matthew
AU - Feron, Eric
N1 - KAUST Repository Item: Exported on 2021-12-14
PY - 2021/5/25
Y1 - 2021/5/25
N2 - This paper investigates stability analysis for implicit, switched linear systems using homogeneous Lyapunov functions (HLF). HLFs of increasing degree are constructed through an outer-product, lifting transformation of the state vector to higher dimensions. This paper presents linear matrix inequalities sufficient conditions for asymptotic stability of these systems based on HLFs. A method is provided to search for Lyapunov functions by incrementally increasing the degree of the homogeneous Lyapunov functions. To address the dimensional growth of the problem space incurred by the lifting transform, a method for dimensional reduction is derived.
AB - This paper investigates stability analysis for implicit, switched linear systems using homogeneous Lyapunov functions (HLF). HLFs of increasing degree are constructed through an outer-product, lifting transformation of the state vector to higher dimensions. This paper presents linear matrix inequalities sufficient conditions for asymptotic stability of these systems based on HLFs. A method is provided to search for Lyapunov functions by incrementally increasing the degree of the homogeneous Lyapunov functions. To address the dimensional growth of the problem space incurred by the lifting transform, a method for dimensional reduction is derived.
UR - http://hdl.handle.net/10754/670633
UR - https://ieeexplore.ieee.org/document/9482717/
UR - http://www.scopus.com/inward/record.url?scp=85111936519&partnerID=8YFLogxK
U2 - 10.23919/ACC50511.2021.9482717
DO - 10.23919/ACC50511.2021.9482717
M3 - Conference contribution
SN - 9781665441971
SP - 2309
EP - 2314
BT - 2021 American Control Conference (ACC)
PB - IEEE
ER -