TY - GEN
T1 - On stability of hybrid systems with random switching
AU - Zhu, C.
AU - Yin, G.
AU - Song, Q. S.
PY - 2006
Y1 - 2006
N2 - This work is concerned with stability of hybrid systems. The hybrid systems that we are interested in are random-switching systems of differential equations. This work presents the formulation of regime-switching systems, recalls the notion of stability, and provides sufficient conditions in terms of Liapunov function. Then the main results including easily verifiable conditions for stability and instability of systems arising in approximation are established. Using a logarithm transformation, necessary and sufficient conditions are derived for systems that are linear in the continuous state component. Several examples are given for demonstrations. It should be noted that somewhat different behavior than the well-known Hartman-Grodman theorem is observed.
AB - This work is concerned with stability of hybrid systems. The hybrid systems that we are interested in are random-switching systems of differential equations. This work presents the formulation of regime-switching systems, recalls the notion of stability, and provides sufficient conditions in terms of Liapunov function. Then the main results including easily verifiable conditions for stability and instability of systems arising in approximation are established. Using a logarithm transformation, necessary and sufficient conditions are derived for systems that are linear in the continuous state component. Several examples are given for demonstrations. It should be noted that somewhat different behavior than the well-known Hartman-Grodman theorem is observed.
UR - https://www.scopus.com/pages/publications/84940643946
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84940643946&origin=recordpage
M3 - RGC 32 - Refereed conference paper (with host publication)
SN - 9781604237924
VL - 1
SP - 177
EP - 184
BT - 44th Annual Allerton Conference on Communication, Control, and Computing 2006
PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
T2 - 44th Annual Allerton Conference on Communication, Control, and Computing 2006
Y2 - 27 September 2006 through 29 September 2006
ER -