Chaotic Characteristics of Discrete-time Linear Inclusion Dynamical Systems

Given K real d-by-d nonsingular matrices S 1, . . . , S K , by extending the well-known Li-Yorke chaotic description of a deterministic nonlinear dynamical system, to a discrete-time linear inclusion/control dynamical system xn ∈ {S 1, . . . , S K} xn−1, x0 ∈ R d and n ≥ 1, we study the irregularity of orbit (xn(x0, σ))n≥1, governed by the law σ : N → {1, . . . , K}, for any initial state x0 ∈ Rd. A sufficient condition is given so that for a residual subset of the space of all possible switching laws σ, we have