On Decentralized Control of Complex Feedback Systems

In this paper, we study the stability and performance robustness of composite feedback systems under decentralized control. It is shown that if the perturbed system transfer matrix is a composite H-matrix for every s on the Nyquist contour, then stabilization of the diagonal blocks of the composite system implies stabilization of the overall system provided the number of unstable poles of the composite system coincide with those of the diagonal blocks. This is then used to define dcentralized controllers for robust stability. When restricted to regular multivariable systems, the new criterion leads to an interesting and simple condition on the peak magnification factor M p of the closed loop system.