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Time scale decomposition of linear implicit singularly perturbed systems

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1 Author(s)
Khalil, H. ; Michigan State University, East Lansing, MI, USA

An implicit singularly perturbed system \dot{x} = A(\epsilon)x , where A(0) is singular, is considered. This note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales. The decomposed form of the system is used to construct a uniform asymptotic approximation to \exp (A(\epsilon)t) .

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Automatic Control, IEEE Transactions on  (Volume:29 ,  Issue: 11 )