2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113933Novel 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.LaTeX, 11 pages, 2 figuresOptimization and ControlDynamical Systems93B05, 93B07, 93B15, 93B40text