October 17, 2014 / by George Council / In booklist

Dynamics at a Switching Intersection: Hierarchy, Isonomy, and Multiple Sliding

If a set of ordinary differential equations is discontinuous along some threshold, solutions can be found that are continuous, if sometimes multivalued. We show the extent to which unique solutions can be found in general cases when the threshold takes the form of finitely many intersecting manifolds.

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October 17, 2014 / by Shai Revzen / In booklist

Control Lyapunov for Hybrid System

A relatively interesting paper presented in IEEE Transactions on Automatic Control, it presents an argument for extending Control Lyapunov Functinos, a standard result for smooth equations, to discrete-time hybrid systems. As gaining insight from the 'raw' dynamics of a hybrid system can be challenging at best, adding a tool to reduce the complexity of analysis, much like Lyapunov theory for ordinary systems, is appealing.

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