The convex integrated design (CID) method: necessary and sufficient conditions for existence of solution

Recently, a convex approach to solve the simultaneous mechanical structure and control system design, referred to as convex integrated design (CID) method, was proposed. This method can successfully solve the problem of integrated system design, in which the mechanical structure parameters, the controller structure and control gains, are simultaneously determined. Despite its effectiveness in solving the integrated system design problem, tie CID method may yield an integrated system design problem that has no solution. The reason for this is analyzed in this paper, and the necessary and sufficient conditions for a solution to the integrated system design problem by CID method are proved mathematically. Simulation results based on an experiment conducted on a linear positioning system are given in this paper and validate the proposed theorem in this paper.