Document Type



This item is available under a Creative Commons License for non-commercial use only


Applied mathematics, Electrical and electronic engineering

Publication Details

Journal of Nonlinear Science, 14, 2004, pp 405-414; DOI: 10.1007/s00332-004-0617-5


Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.