Echo state property: spectral-radius rho(W) < 1 via Perron-Frobenius on |W|

Echo state property via Perron-Frobenius. Setup: a reservoir-computing network x(t+1) = tanh(W*x(t) + W_in*u(t)) needs the echo state property (ESP) - that for any two different initial conditions x0, x0', the difference |x(t) - x'(t)| ->…