Decentralised Robust Controller Synthesis For Discrete-Time Polytopic Systems With Additive Uncertainty Using An Iterative-Lmi Approach

In this paper, we study robust and decentralised controller synthesis for discrete-time polytopic systems with norm-bounded additive uncertainty. To do so, we aim at finding a local solution to an optimisation problem involving bilinear matrix inequality constraints. The local solution is found using an iterative scheme that involves solving an optimisation problem with linear matrix inequality constraints. We will also briefly present and adapt a non-iterative but conservative solution strategy based on linear matrix inequalities and a solution strategy based on a so-called cone complementarity linearisation to compare our proposed method to. Finally, we will illustrate the solution strategy and show that it reduces conservatism in the controller synthesis on two decentralised controller synthesis examples, and on an example of networked control of a chemical batch reactor.