Analysis of hybrid systems resulting from hysteresis and saturation: a {L}yapunov approach
Submitted by ricardo on February 28, 2017 - 2:36pm
Title | Analysis of hybrid systems resulting from hysteresis and saturation: a {L}yapunov approach |
Publication Type | Conference Paper |
Year of Publication | 2008 |
Authors | Dai D., Sanfelice R.G, Hu T., Teel A.R |
Conference Name | Proc. 47th IEEE Conference on Decision and Control |
Keywords | hybrid systems |
Abstract | This paper studies a class of hybrid systems with linear (or linear plus saturated linear) continuous and discrete dynamics, which are determined by a ?ow map and jump map, and state-triggered jumps. One motivation for considering this class of systems is that they can model control systems with a relay-type hysteresis element. Based on Lyapunov theorems for hybrid systems, a Lyapunov function is constructed that effectively incorporates the feature of the jumps. Global asymptotic stability analysis is presented for the case when the ?ow map is linear, and local asymptotic stability analysis is presented for the case when the ?ow map is linear plus saturated linear. The stability conditions are derived as matrix inequalities. A numerical example is presented to illustrate the hybrid modeling process for a system experiencing hysteresis. Simulations con?rm the effectiveness of the proposed analysis tools and demonstrate the potential of the Lyapunov function. |
URL | https://hybrid.soe.ucsc.edu/files/preprints/32.pdf |
DOI |