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A converse Lyapunov theorem for a class of dynamical systems which undergo switching. (English) Zbl 0960.93046
The paper considers mainly linear polysystems arising from dynamical systems undergoing switches x ˙=A γ x, where γΓ is the range of the swtiching path s: + Γ, s(·) being a piecewise constant function. For such systems converse Lyapunov theorems are obtained in the case of exponential stability. The interesting feature of the paper is that sometimes the Lyapunov function may fail to be quadratic and an upper bound on its degree has not yet been found.
MSC:
93D20Asymptotic stability of control systems
34D20Stability of ODE
93D30Scalar and vector Lyapunov functions