University of Twente Student Theses


Stability analysis of planar switched linear systems

Stuiver, Paul (2020) Stability analysis of planar switched linear systems.

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Abstract:This paper provides stability conditions for a planar switched linear system having two subsystems that are asymptotically stable. The key issue is that even though both subsystems are stable, the switched system may be unstable by switching at particular moments. Asymptotic stability under arbitrary switching can be proved by showing the existence of a common Lyapunov function (CLF). This type of stability can also be proved when the matrices of the subsystems commute. If the switched system does not have a CLF, the system must stay ’long enough’ in each location to ensure stability. This is also known as the dwell time. A formula on the minimum dwell time for the switched system is provided. It will turn out that the formula is rather conservative and restrictive. Therefore another formula on the minimum dwell time is provided.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics BSc (56965)
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