Technical communique: FIR stabilization in discrete one-sided model-matching problems
Automatica (Journal of IFAC)
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This paper studies continuous-time $H^2$ feedforward tracking and estimation problems with FIR (finite impulse response) solutions. Both causal and noncausal solutions are considered. It is shown that these problems can be treated as special cases of static problems in the lifted domain, which, in turn, can be solved in terms of a two-point boundary value (Hamilton-Jacobi) system. This results in fixed-dimension closed-form solutions. A numerically stable form of these solutions, which uses matrix exponentials of Hurwitz matrices only, is also derived.