Finite zeros of positive linear discrete time systems

The notion of finite zeros of discrete-time positive linear systems is introduced. It is shown that such zeros are real nonnegative numbers. It is also shown that a square positive strictly proper or proper system of uniform rank with the observability matrix of full column rank has no finite zeros. The problem of zeroing the system output for positive systems is defined. It is shown that a square positive strictly proper or proper system of uniform rank with the observability matrix of full column rank has no nontrivial output-zeroing inputs. The obtained results remain valid for non-square positive systems with the first nonzero Markov parameter of full column rank.