Polynomial methods for direct SD system design

Abstract

Immediate utilization of the formulae given in Chapter 17 for the direct design of feedback sampled-data systems involves some technical difficulties. This results from the fact that the coefficients of the functionals to be minimized depend on the choice of the basis stabilizing pair a°(ζ),b°(ζ) Even though the final result does not depend, from the theoretical viewpoint, on the choice of this pair, this procedure is very important for practical computations, because in many cases the solution is not robust with respect to computational errors in the coefficients of the polynomials a° and b°. Therefore, for practical design it is desirable to use a minimization technique that does not use the polynomials a° and b° and is numerically stable. For this purpose we have to eliminate a°,b° and the parameter-function ø(ζ) from the equations of Chapter 17, which determine the optimal controller. Various conducting of such procedures are considered in Rosenwasser et al. (1996); Rosenwasser (1995b).