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Conditions on the stability of a class of second-order switched systems

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4 Author(s)
Akar, M. ; Hamilton Insitute, Nat. Univ. of Ireland, Maynooth, Ireland ; Paul, A. ; Safonov, M.G. ; Mitra, U.

For a special class of systems, it is shown that the existence of a common quadratic Lyapunov function (CQLF) is necessary and sufficient for the stability of an associated switched system under arbitrary switching. Furthermore, it is shown that the existence of a CQLF for N (N>2) subsystems is equivalent to the existence of a CQLF for every pair of subsystems. An algorithm is proposed to compute a CQLF for the subsystems, when it exists, using the left and right eigenvectors of a critical matrix obtained from a matrix pencil.

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Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 2 )