A switching signal for a switched system is said to be shuffled if all modes of the are activated infinitely often. In this paper, we develop tools analyze stability properties discrete-time linear systems driven by signals. We introduce new notion joint spectral radius (SJSR), which intuitively measures how much state contracts each time shuffles (i.e. have been activated). show relates associ...

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities – the lower spectral radius and the largest Lyapunov exponent – are not algorithmically approximable.