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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.
Date of Publication: Feb. 2006