Persistent excitation in bilinear systems

Discrete-time systems described by difference equations which are polynomial in the input and linear in the output are discussed. Bilinear systems are special members of this class. Two issues are examined. First, a multidimensional polynomial-based algebraic condition which is necessary and sufficient for such systems to be identifiable is given. Second, subject to an identifiability assumption, a condition on the input sequence which guarantees persistent excitation is given. The principle analytic tool used in this study involves multidimensional polynomials