LAUSR

known and finite set of possibilities. For example, the motion of a vehicle system that moves according to linear (or linearized) laws of physics and a program that picks the control inputs, like throttle and steering, every so often, from a finite bank of possibilities. The paper gives a sharp result showing the entropy of such systems, for all possible switchings, can be computed exactly in terms of the joint spectral radius of those finite set of system matrices. This result adds to our knowledgebase an expressive class of systems for which entropy can be calculated. I recommend the theoretically inclined readers to read the short proof that uses a couple of equivalent definitions of entropy and properties of the joint spectral radius. The latter object is well-studied and can be calculated using numerical analysis toolboxes. The paper is also interesting because it gives a practical sensor-estimator algorithm for implementing state estimation for switched linear systems, and the data rate used matches the entropy bound. What can we expect to see in the future? Following on this line of research, one obvious next step would be to get data rate lower bounds for controlling different classes of switched systems. The current methods require calculation of derivatives and Jacobians, which curtails their application in realistic simulation models that often use heterogeneous numerical analysis functions. A fruitful research direction would be to combine the topological entropy methods with automated differentiation techniques, to get practical data rate bounds from simulation programs.