Decomposition and Simultaneous Projection Methods for Convex Feasibility Problems with Application to robustness Analysis of Interconnected Uncertain Systems

In this paper a specific class of convex feasibility problems are considered and tailored algorithms to solve this class of problems are introduced. First, the Nonlinear Cimmino Algorithm is reviewed. Then motivated by the special structure of the problems at hand, a modification to this method is proposed. Next, another method for solving the dual problem of the provided problem is presented. This leads to similar update rules for the variables as in the modified Nonlinear Cimmino Algorithm. Then an application for the proposed algorithms on the robust stability analysis of large scale weakly interconnected systems is presented and the performance of the proposed methods are compared