Combinatorial Optimization Approach to Coarse Control Quantization

In this paper we consider the problem of stabilization of a single input linear discrete time invariant system where the control can take values from a countable set. The problem definition includes the design of a quantization scheme that will produce the coarsest such set while guaranteeing stability. This problem is cast as a static combinatorial resource allocation or coverage problem where in the control values are viewed as resources which have to cover the state space. A relaxed notion of stability is used to represent the coverage cost function. The resulting quantizer on applying deterministic annealing algorithm is logarithmic and explicitly gives the partition of the state space