On the reliable decentralised stabilisation of n MIMO systems

In this paper, we consider the problem of reliable decentralised stabilisation for n multi-input multi-output (MIMO) systems when some of the shared controllers among these systems are faulty, in the sense that they fail to operate properly due to subsystem (module) failures that may occur in actuators, sensors or controllers. Specifically, we present a design framework using a dilated linear matrix inequalities (LMIs) technique for deriving reliable stabilising state-feedback gains for all n MIMO systems; while a set of decentralised unknown disturbance observers (UDOs) that are shared by all n MIMO systems is used for extending the result to the output-feedback case. Moreover, a sufficient condition for the solvability of the set of decentralised UDOs is given in terms of a minimum-phase condition of each subsystem and a lower-bounding condition on the number of outputs of each channel. We also present a numerical example that illustrates the applicability of the proposed technique.