Model reduction by balanced truncation of dominant systems

Alberto Padoan, University of Cambridge


The talk presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. 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 exploiting 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 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. A model reduction method is then developed and shown to preserve p-dominance and p-dissipativity properties, with an explicit bound on the approximation error being available. The method is illustrated by means of simple examples and the potential of the proposed framework is illustrated by the analysis and design of multistable and oscillatory Lur’e feedback systems.