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First, we give a necessary condition for a proportional\u2013integral controller to stabilize the process with certain constant delay using Descartes\u2019 rule of signs. Then by employing the generalization of the Hermite\u2013Biehler theorem applicable to quasi-polynomials, a complete set for all stabilizing proportional\u2013integral parameters is derived to stabilize the open-loop stable and unstable systems. In the case of uncertain time delay, we provide a design approach to stabilize the related plant with a robust proportional\u2013integral controller, where the unknown but constant time delay lies inside a known interval. Three examples illustrate the effectiveness of the proposed results. <\/jats:p>","DOI":"10.1177\/0959651814520826","type":"journal-article","created":{"date-parts":[[2014,2,22]],"date-time":"2014-02-22T03:47:12Z","timestamp":1393040832000},"page":"393-405","update-policy":"http:\/\/dx.doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["All stabilizing sets for proportional\u2013integral controller of high-order delay processes"],"prefix":"10.1177","volume":"228","author":[{"given":"Honghai","family":"Wang","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang, P.R. China"},{"name":"State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, P.R. 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