Quasi-finite-rank approximation of compression operators based on L∞[0, h]-induced norm

This paper deals with an approximation problem of compression operators, which play important roles in the operator-theoretic approach to sampled-data systems and time-delay systems. More precisely, we study a method for quasi-finite-rank approximation of compression operators in the L
^∞
[0, h]-induced norm sense. We apply the idea of the Fast-Sample/Fast-Hold (FSFH) approximation technique, and show that the approximation problem can be transformed into such a linear programming problem that asymptotically leads to optimal approximation as the FSFH approximation parameter M tends to infinity. Finally, numerical examples are given to demonstrate the effectiveness of the apprxoimation technique.