Stabilization of linear systems with limited information multiple input case

This paper is motivated by the question of control with communication constraints, a topic that has recently generated significant interest. In this paper, we restrict ourselves to the problem of computing the coarsest state information required to stabilize a MIMO discrete linear time invariant system. The formulation is motivated by the recent work of Elia et al. (2001), which deals with the single-input case and the development here is an attempt to generalize it to the the multi-input setting. Unlike the single-input situation, we now have the option of using multiple inputs even when the system is controllable through a single (fictitious) input possibly obtained by a linear combination of the actual inputs. This question is related to the computation of the coarsest quantization for a system decomposed along its invariant subspaces (or a decoupled set of systems). It turns out that coarsest quantization is a covering of the entire space with ellipsoids, implying that we can do significantly better than quantizing each invariant subspace (or each decoupled system) separately.