Applications are invited by well-qualified applicants for an MSc position in the area of reachability analysis of positive dynamical systems.

Positive dynamical systems provide the natural modeling framework for diverse applications in areas including Communications, Biology and Economics.  Essentially, a positive dynamical system is one in which the state variables are constrained to remain nonnegative for all time.  Systems of this class possess a number of very specific properties and their analysis has long been a fertile area of research within general systems theory.  At the current time there is a well-developed theory of positive linear time-invariant (LTI) systems; however many modern applications in Communications and Bio-medical engineering require extensions of this theory to incorporate more realistic time-varying and nonlinear models.  The aim of this project is to contribute to the state of the art in this area by developing results and tools for analysing the reachability properties of time-varying, and in particular, switched positive systems.  While the reachability properties of positive LTI systems have received considerable attention in the literature, to date relatively little has been written on the reachability properties of positive switched systems.  This project will explore the geometric properties of the reachability set for positive switched systems and investigate the possibility of obtaining useful necessary and sufficient conditions for reachability of positive switched systems.  

Applicants should have excellent mathematical and analytic skills and possess a solid background in linear algebra and advanced calculus. Familiarity with mathematical control theory would also be an advantage.

The Hamilton Institute is committed to research excellence. This post offers an exciting opportunity for successful candidates to tackle fundamental research problems within a stimulating multi-disciplinary research environment with state of the art facilities and strong links to the international research community.

MSc Stipend: €21000 (tax free)

To apply, candidates should submit a detailed CV, transcripts of undergraduate grades, motivation letter, and the names and addresses of two referees for letters of recommendation to: hamilton@nuim.ie. Informal enquiries to Dr. Oliver Mason (oliver.mason@nuim.ie)

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