On the perturbation of bimodal systems
نویسندگان
چکیده
Given a bimodal system defined by the equations { ẋ(t) = A1x(t) + Bu(t) if cx(t) ≤ 0 ẋ(t) = A2x(t) + Bu(t) if cx(t) ≥ 0 (1) where B ∈Mn,m and Ai ∈Mn, i = 1, 2, are such that A1, A2 coincide on the hyperplane V =Kerc. We consider in the set of matrices defining the above systems the simultaneous feedback equivalence defined by ([A1, B], [A2, B]) ∼ ([A1, B′], [A2, B′]) if [Ai B ′] = S−1[Ai B] [ S 0 R T ] i = 1, 2 with S(V) = V This equivalent relation corresponds to the action of a Lie group. Under this action we obtain, in the case m ≤ 1, the semiuniversal deformation, following Arnold’s technique. Then the problem of structural stability is studied.
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