Singular perturbation in piecewise-linear systems |
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Authors: | Heck BS Haddad AH |
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Affiliation: | Sch. of Electr. Eng., Georgia Inst. of Technol., Atlanta, GA; |
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Abstract: | A singular perturbation technique is developed that allows for a decoupling of a continuous piecewise-linear system into slow and fast subsystems. Under the assumption of asymptotic stability, the fast variable is found to decay in the boundary layer to its quasi-steady-state solution, which is given by a continuous implicit function of the slow variable. The solution is found using a finite step algorithm. Sufficient conditions for the approximation to be accurate to an order of O(μ), where μ is a parameter of the system, are given. The technique is illustrated by a numerical example |
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