Nonlinear systems - Algebraic gramians and model reduction

Purpose - Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and observability gramians for the corresponding bilinear system. Such gramians form the core of model reduction schemes involving balancing. Design/methodology/approach - The paper examines certain properties of the bilinear system and identifies parameters that capture important information relating to the behaviour of the system. Findings - Novel approaches for the determination of approximate constant gramians for use in balancing-type model reduction techniques are presented. Numerical examples are given which indicate the efficacy of the proposed formulations. Research limitations/implications - The systems under consideration are restricted to the so-called weakly nonlinear systems, i.e. those without strong nonlinearities where the essential type of behaviour of the system is determined by its linear part. Practical implications - The suggested methods lead to an improvement in the accuracy of model reduction. Model reduction is a vital aspect of modern system simulation. Originality/value - The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design of radio-frequency integrated circuits.