$L_2$-optimization and fixed poles for sampled-data systems with generalized hold

This paper considers the $L_2$-optimization problem for a standard sampled-data system with generalized hold of an arbitrary order. The original problem is reduced to the minimization problem of a degenerate quadratic functional, where solution appears nonunique. And finally, the authors propose a polynomial procedure for constructing a set of optimal discrete causal controllers and establish some relevant properties of $L_2$-optimal systems in the context of applications.