Connective stability of discontinuous interconnected systems via parameter dependent Lyapunov functions

Connective stability is defined for a discontinuous interconnected system under structural perturbations. Stability conditions are obtained using both Lipschitz and C/sup 1/-type vector Lyapunov functions. The functions are chosen to be parameter dependent in order to handle uncertainties in the interconnections. Connective stability conditions are converted to convex optimization problems via theory of M-matrices. As an illustration of the obtained results it is shown that generalized matching conditions apply to stabilization of systems with piecewise-continuous interconnections.