Lower bound analysis of H∞ performance achievable via decentralized LTI controllers

This paper is concerned with the decentralized H∞ controller synthesis problem for discrete-time LTI systems. Despite of intensive research efforts over the last several decades, this problem is believed to be nonconvex and still outstanding in general. Therefore, most of existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficulty, in this paper, we propose convex optimization procedures for computing lower bounds of the H∞ performance that is achievable via decentralized LTI controllers of any order. In particular, we will show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting.We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization.