Given a stable square plant G(1)(s), based on linear matrix inequality (LMI) method, necessary and sufficient conditions are presented for the existence of a stable multiplier G(2)(S) such that G(1)(s)G(2)(S) is extended strictly positive real (ESPR). Furthemore, for uncertain plants, the corresponding problems are considered and solved. An application to the study of dichotomy for pendulum-like systems is also presented. Examples are given to illustrate the results.