Abstract
Novel constructions of empirical controllability and observability gramians for nonlinear systems are proposed for subsequent use in a balanced truncation style of model reduction. 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.
Original language | English |
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Pages (from-to) | 405-414 |
Number of pages | 10 |
Journal | Journal of Nonlinear Science |
Volume | 14 |
Issue number | 5 |
DOIs | |
Publication status | Published - Oct 2004 |
Externally published | Yes |
Keywords
- Lyapunov equation