Decentralized quadratic stabilization of interconnected descriptor systems

This paper considers the problem of quadratic stabilizability for a class of interconnected descriptor systems such that each subsystem is represented in the descriptor form and parametric uncertainties lie in all system matrices of the subsystems and also in interaction gains among subsystems. Quadratic stability requires here that the interconnected descriptor system has neither unstable finite modes nor impulsive modes. This paper presents a sufficient condition under which the interconnected descriptor system is quadratically stabilizable via decentralized static feedback. The condition is given in terms of matrix inequalities on the subsystem level and an M-matrix constraint for the matrix consisting of the upper bounds of the interaction gains