Research

Robust dominance theory

Robustness is a classical concept in engineering. In broad terms, a behavior is robust if it persists under the effect of exogenous perturbations or parametric uncertainty. The analysis and design of robust stability of a system is nowadays a classical subject in control theory. However, a theory of robustness is lacking for behaviors away from equilibria, including the ubiquitous switches and oscillators arising in nature and engineering.

Robust dominance theory is an interconnection theory geared towards the analysis and design of systems that switch and oscillate. The theory demonstrates that such systems can be studied and engineered using familiar frequency domain tools and convex optimization.

A geometric approach to modelling and approximation

With the rapid advance of computer and communication technologies, mathematical models of dynamical systems are playing an increasingly important role for analysis and design. The need of precision frequently leads to the inclusion of a large number of variables, thus posing a serious obstacle to achieving accurate simulations. Model reduction methods alleviate this issue by constructing simplified models that capture prescribed features of the original system, while system identification methods allow to build these models directly from measured data.

The goal of geometric modelling and approximation is to develop a theory of model reduction and system identification based on the differential geometric approach to nonlinear systems, which has significantly impacted on both theory and applications in many control problems.

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