Shift Operator Induced Approximations of Delay Systems
Pertti M. Mäkilä, Jonathan R. Partington · SIAM Journal on Control and Optimization · 1999
Certain shift operator induced finite-dimensional approximations of an important class of delay systems are studied. $H_\infty$, H 2 and L 1 error bounds are given for stable delay systems. Furthermore, a multiple shift formula, generated by a second-order Padé shift, is analyzed further, and an exact asymptotic $H_\infty$ error formula is derived. The studied class of shift operator induced approximations provides an appealing and most transparent approach for determining good finite-dimensional models of delay systems.