Nowadays,theresearchersintoControlTheoryanditsApplicationsaswellas Matrix Analysisare well awareand recognizethe importanceof PositiveS- tems. This volume contains the proceedings of the "Third Multidisciplinary Symposium onPositiveSystems:Theory andApplications (POSTA09)" held in Valencia, Spain, September 2-4, 2009. At present, this is the only world congress whose main topic is focused on this ?eld. After this third event, we thinkthatwehaveestablishedthebasisofaregulartriennialeventsupported in the task of the previous organizing committees and hope to have met the requirements of their expectations. This POSTA09 meeting has been organized by members of the "Univ- sitat Polit' ecnica de Val' encia", who have taken their doctor's degree in the subjects of the conference. We are grateful to all of them for their ent- siasm, e?ort and especially their collaboration, without the help of which the outcome would have never been the same. Also, we highly appreciate Christian Commault for having his experience at our disposal. Besides that, we wish to thank the International Programme Committee components and additional referees for their outstanding work in the review process of the contributions. We are happy to say that their constructive suggestions and positive comments have improved the quality of the presentations. We are very much obliged to the following organizations for having- nancially backed this congress: "Ministerio de Educaci' on y Ciencia", "C- selleriad'Educaci' odelaGeneralitatValenciana","UniversitatPolit' ecnicade Val' encia(UPV)"and"SociedadEspano " ladeMatem' aticaAplicada(SEMA)".