Performance bounds on the control of highly sparse discrete-time multivariable systems

This study deals with achievable performance bounds in the control of multivariable systems having a high degree of sparsity. The systems to be considered are square, linear, stable, time-invariant and discrete-time, and it is assumed that they can be reasonably described by a matrix transfer function, which is diagonal plus one or two off-diagonal elements. The performance is quantified using the 2-norm of the weighted loop sensitivity. The starting point is the achievable performance bound for the decentralised control of a diagonal model. Then, under the assumption that an available sparse model is a better model for the plant, the new achievable performance bound is calculated based on this latter model. With these results, the significance of basing the control design on a model which is more complex than the diagonal one, is assessed.