Decoupling and Order Reduction for Linear Time-Varying Two-Time-Scale Systems

摘要

The class of time-varying linear systems which are two-time-scale on an interval may be decoupled by a time-varying transformation of variables into separate subsystems containing the slow and fast dynamic parts. The transformation is obtained by solving a nonsymmetric Riccati differential equation forward in time and a linear matrix differential equation backward in time. Small parameters are identified which measure the strength of the time scale separation and the stability of the fast subsystem. As these parameters go to zero, the order of the system is reduced and a useful approximate solution to the original system is obtained. The transformation is illustrated for examples with strong and weak fast subsystem stability. (Author)