Using the method of aggregate modeling, the paper derives an approximation of the rotary pendulum's Euler-Lagrange dynamics within a specified operating region. Based on the resulting aggregate model, the authors cast the system's stabilization as a feasibility problem associated with linear matrix inequalities. Furthermore, the authors test the resulting stabilizing controller on the actual rotary pendulum and verify the expected results experimentally.
Aggregate modeling can approximate the convex hull of local matrices to nonlinear dynamics for any given accuracy. The authors use aggregate models to extend sufficient conditions for asymptotic stability of linear differential inclusions to nonlinear dynamics. An example illustrates the applicability of the proposed criteria to the analysis of nonlinear biochemical reaction chains.
A Unified Stochastic Hybrid System Approach to Aggregate Modeling of Responsive Loads
