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FLOW BALANCING NONLINEAR SYSTEMS

This paper introduces a novel approach towards balancing of nonlinear systems. It differs from other approaches in two key ideas: The first is the observation that linear timeinvariant systems have a single equilibrium point (the origin), and that the balanced realization for the class of a linear timeinvariant systems essentially relates to this equilibrium. This sparked the idea to consider balancing in general as a property associated with invariant sets of a given nominal flow. The second idea is to define a notion of global balancing as the one that commutes with linearization. The existence and construction of balanced and uncorrelatedrealizations are discussed. Uncorrelatedness is a relaxed notion of balancedness, introduced here. Several examples, including the Van der Pol oscillator are shown.