On the discretisation of sparse linear systems

This paper addresses the discretisation problem for sparse linear systems. Classical discretisation methods usually destroy sparsity patterns of continuous-time systems, since they do not consider structural constraints. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem adequately, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices that arise in practical applications. Numerical examples are included.