'had a positive influence' is correct and usable in written English.
For example: The teacher had a positive influence on her students, inspiring them to achieve their goals.
Biaxial loading had a positive influence on fatigue lives.
(1966; Phenomenology: Metaphysics or Method?), also had a positive influence.
He knows Arsenal had a positive influence on his career.
It has also had a positive influence on shaping the detail of those changes.
Aaron Mauger [the head coach] has come in and had a positive influence.
G. mosseae had a positive influence on healthy C. roseus plants and S. citri infection.
Furthermore, the number of host plants had a positive influence on butterfly diversity and density.
Higher ion concentration had a positive influence on the deposition process and allowed to achieve a higher deposition rate.
Also, pre-straining of coating specimens had a positive influence on the recoverability of their strain sensitivity.
Results suggested that cultural diversity had a positive influence on decision-making and a negative influence on communication.
Experimental results confirmed that SMCT had a positive influence on pre-cooling, preservation quality and physicochemical properties of cucumbers.
