Sign Controllability of a Nonnegative Matrix and a Positive Vector

An n-by-n matrix A and a vector b are controllable if and only if the matrix [ b,Ab,A² b, … ,An - 1 b ] has rank n. An array with each entry equal to +, –, or 0 is a sign pattern. If A and B are sign patterns of orders n-by-n and n-by-1, respectively, then the pair ( A, B ) is called sign controllable if $( A,b )$ is controllable for all A ∈ A and for all b ∈ B . Sign controllability of a nonnegative sign pattern A and a positive sign pattern B are characterized, and sufficient conditions for other cases of the sign controllability problem are given.