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Switched linear systems and infinite products of matrices
Pablo A. Parrilo
Massachusetts Institute of Technology, United States of America
Many situations of interest can be modeled as "switched linear systems", which are collections of linear difference equations, with some logical rule for switching between subsystems. Mathematically, this boils down to understanding infinite products of matrices, all of which are elements of a given finite set. Analyzing these systems is a difficult question that appears in a number of applications, including the analysis of optimization algorithms, information theory, and wavelets. Depending on whether the switching is deterministic or stochastic, different notions can be used to quantify the resulting convergence rate, like the joint spectral radius, or the Lyapunov exponent. In this talk, we provide a gentle introduction to this class of problems, their applications, and several results regarding their exact and approximate computation.
