Design of sensitivity and round-off noise optimal state-space discrete systems

Abstract

A previously defined sensitivity measure for state-space realizations is used, and the attainable minimum value and its necessary and sufficient conditions are given. An explicit optimization procedure which evaluates the complete class of realizations with minimum sensitivity is proposed. Conditions for minimizing the sensitivity under an 1, dynamic range constraint are established and an explicit method for obtaining this minimum is given. Since the relation between this sensitivity measure and the noise power gain for I, scaled digital filters can be given, and since the main part of the optimization can be carried out without taking into account the dynamic range constraint, a simple procedure for simultaneous minimization of sensitivity and round-off noise is obtained. A numerical example is given to exemplify the computational procedure.