Abstract

The talk presents a quantitative robustness analysis framework geared towards the analysis and design of systems that switch and oscillate. This is motivated by the fact that, while such phenomena are ubiquitous in nature and in engineering, model reduction methods are not well developed for behaviours away from equilibria. Our framework addresses this need by extending recent advances on p-dominance theory and p-dissipativity theory, which aim at generalising stability theory and dissipativity theory for the analysis of systems with low-dimensional attractors. We first prove a robust Nyquist theorem for p-dominance. Then we discuss a generalisation of balanced truncation to linear dominant systems. From a mathematical viewpoint, balanced truncation requires the simultaneous diagonalisation of the reachability and observability gramians, which are positive definite matrices. Within our framework, the positivity constraint on the reachability and observability gramians is relaxed to a fixed inertia constraint: one negative eigenvalue is considered in the study of switches and two negative eigenvalues are considered in the study of oscillators. The proposed framework is illustrated by means of a textbook electro-mechanical example.