This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not.
|Title of host publication||Proceedings of the 18th international symposium on mathematical theory of networks & systems|
|Place of Publication||USA|
|Number of pages||11|
|ISBN (Print)||not assigned|
|Publication status||Published - Aug 2008|
Daws, C. F., Langerak, R., & Polderman, J. W. (2008). Decision algorithm for the stability of planar switching linear systems. In Proceedings of the 18th international symposium on mathematical theory of networks & systems (pp. 11). USA: SIAM.