Global stability and robustness analysis of oscillators with application to biology and robotics

点击翻译按钮获取中文摘要

In this research project, we propose the creation of two new global analysis methodologies which can be seen as part of a first set of elements and tools for obtaining a general system theory for oscillators. These methodologies will then be used to implement two algorithms aimed at numerically proving existence and global asymptotic stability of limit cycle oscillations generated by complex (high dimensional) models of oscillators, and at studying their robustness and parameter sensitivity. The new methodologies that we propose to explore in depth in this project will rely on the recent research results of the PI and the RA. The first methodology will generalise the piecewise linear systems numerical analysis methodology developed by the PI. On the other hand, the second methodology will explore the possibility of reformulating all dissipativity conditions appearing in the passive oscillator theorems proposed by the RA in terms of Integral Quadratic Constraints for which efficient numerical verification algorithms already exist.