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Applied mathematics, Electrical and electronic engineering
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.
M. Condon and R. Ivanov, On the empirical balanced truncation for nonlinear systems, Journal of Nonlinear Science, 14, 2004, pp 405-414; DOI: 10.1007/s00332-004-0617-5
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