Design of robust decentralised controllers for MIMO plants with delays through network structure exploitation

A methodology is proposed for the design of robust controllers for retarded and neutral-type time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of spectral abscissa and H∞ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO systems is presented, which imposes a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, if the system to be controlled has the structure of a network of coupled identical subsystems, then it is shown that this structure can be exploited by an improved algorithm for the design of decentralised controllers, thereby improving computational efficiency and scalability with the number of subsystems. Several numerical examples illustrate the effectiveness of the methodology, and its extension towards consensus type problems.