Synthesis of complete rational orthonormal bases with prescribed asymptotic order

In this paper, a method to construct complete rational orthonormal model se ts with prescribed asymptotic order is presented for continuous-time system s. Two special cases that illustrate the application of the method are stud ied. In the first case, this method is shown to produce the generalized Lag uerre functions which form a complete model set for H-2 and have asymptotic order two. In both eases, this method is equivalent to calculating Toeplit z determinants generated by a rational function. The latter problem is redu ced to finding solution of a linear finite-difference equation. (C) 2001 El sevier Science Ltd. All rights reserved.