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Stability, Synchronisation and Model Reduction in Nonlinear Systems

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In this talk, I will discuss three topics that we have recently developed in nonlinear systems theory. I will first discuss Generalised Absolute Stability, which is a general method of treating polynomial systems with non-polynomial, uncertain or time-varying feedback. Analysis is completed with sum of squares programming, and this method extends both the applicability of sum of squares as well as existing absolute stability theory. I will also introduce Restricted Partial Stability, the development of which allows improved local and global analysis methods for synchronisation of nonlinear networked systems. The work also allows a common framework for synchronisation analysis of both oscillator networks and power systems. Finally, I will briefly describe a model reduction technique for deriving reduced mechanistic models of gene regulation, as well as discussing applications of the models in system and synthetic biology.

This talk is part of the CUED Control Group Seminars series.

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