Order Reduction of Multi-scale Differential Inclusions
Nonlinear multi-valued differential equations containing several small parameters reflecting different time scales are under consideration. Exponential stability type conditions are presented, under which a re-iterated averaging procedure leads to a reduced order system, whose solution set contains all possible limit trajectories of the slowest subsystem, as the perturbation parameters tend to zero. Approximation rates are given as well. It turns out that the order of approximation does not depend on the number of time scales. However, the convergence is not as fast as in the case of nonlinear ordinary differential equations.
KeywordsExponential Stability Solution Mapping Order Reduction Nonlinear Control System Measurable Selection
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