In this paper, a methodology using small-gain theorem and eigenvalue sensitivity for analyzing the stability of the closed-loop digital control system subject to finite
word length floating point (FWLFP) operations is proposed. The roundoff and computational errors of the observer/controller parameters caused by FWLFP operations are
expressed in function of mantissa bit number. First, a sufficient stability criterion in
terms of the mantissa bit number for the closed-loop system is derived based on small
gain theorem. Then, the magnitude and supplemental angle measures are derived from
the sensitivities of the closed-loop system eigenvalues with respect to observer/controller
parameters, respectively, in the sense of mixed matrix-2/Frobenius norms. Therefore, an
optimal similarity transformation can be obtained from Hermitian solution by considering both the magnitude and supplemental angle measures simultaneously. Based upon the
optimal similarity transformation as well as the stability criterion, a minimum mantissa
bit number for implementing observers/controllers in FWLFP digital computers can be
obtained. The advantages of the proposed methodology are that it can handle the closedloop systems with complex eigenvalues and give an implementable real-valued optimal
similarity transformation by easily algebraic operations. Finally, detailed numerical design processes and simulation results are performed to illustrate the effectiveness of the
proposed scheme.
Relation:
International Journal of Innovative Computing Information and Control
