SIAM Journal on Control and Optimization, Vol.48, No.4, 2433-2460, 2009
IMPOSING FIR STRUCTURE ON H-2 PREVIEW TRACKING AND SMOOTHING SOLUTIONS
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.