A Lyapunov Function Approach to Energy Based Model Reduction

Model reduction based upon the idea of eliminating coordinates with low levels of associated power, energy or activity has been proposed by a number of researchers. None of these results, however, produce the sort of computable bounds on the neglected dynamics that would be useful in the design of controllers with guaranteed robustness properties. This paper outlines an approach to model reduction based upon Lyapunov functions that represent a modified version of the system energy of Lagrangian subsystems. The Lyapunov functions are used to bound the states of subsystems to be removed, enabling these states to be treated as time-varying perturbations in a simplified set of dynamic equations. In contrast to other results in energy-based model reduction, this approach provides bounds on the disturbances caused by the unmodeled dynamics though at the cost of the implementation ease associated with other methods.