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Zbl 0960.93046
Dayawansa, Wijesuriya P.; Martin, C.F.
A converse Lyapunov theorem for a class of dynamical systems which undergo switching.
(English)
[J] IEEE Trans. Autom. Control 44, No.4, 751-760 (1999). ISSN 0018-9286

The paper considers mainly linear polysystems arising from dynamical systems undergoing switches $\dot x= A_\gamma x$, where $\gamma\in \Gamma$ is the range of the swtiching path $s:\bbfR_+\to\Gamma$, $s(\cdot)$ 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 2000:
*93D20 Asymptotic stability of control systems
34D20 Lyapunov stability of ODE
93D30 Scalar and vector Lyapunov functions

Keywords: switched systems; linear polysystems; switches; converse Lyapunov theorems

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