Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.


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Langerak, Rom and Polderman, Jan Willem (2005) Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation. In: 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Sevilla, Spain, Sevilla, Spain.

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Abstract:The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.
Item Type:Conference or Workshop Item
Copyright:©2005 IEEE
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/54781
Official URL:http://tinyurl.com/aq6sbb
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