A note on aperiodicity condition for linear discrete systems. (English) Zbl 0572.93060

Jury, E. I.

IEEE Trans. Autom. Control 30, 1100-1101 (1985).

Conditions for the roots of a real polynomial to lie in the segment [0,1), i.e. aperiodicity conditions are obtained. The conditions are based on a nonlinear transformation which transforms the segment [0,1) onto the periphery of the unit circle. The results of this note correct the earlier proposed corollary obtained by E. Szaraniec [see Automatica 9, 513-516 (1973; Zbl 0257.93027)] using this transformation and present a test for verifying the aperiodicity condition.

MSC:

93D20	Asymptotic stability in control theory
93C05	Linear systems in control theory
93C55	Discrete-time control/observation systems
93B17	Transformations
30C15	Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)

Keywords:

aperiodicity conditions; nonlinear transformation