In this talk, the notion of generating
functions is introduced as a framework to study quantitatively the stability
and stabilizability of switched systems, including
randomly switching systems. Several important quantities, such as the joint
spectral radius, Lyapunov exponent, L2-induced gain, stabilizability index, can be characterized uniformly in
such a framework. Efficient numerical algorithms will be proposed for the
estimations of these quantities. As an example, the application to the
consensus problem on randomly changing networks will be discussed.
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