STABILIZING STATIONARY LINEAR DISCRETE-SYSTEMS - MINIMAL AND BALANCEDEXPANSIONS IN ANY REAL BASE

Let a be a real number strictly greater than 1 and let D be a finite i nterval of Z containing 0. In this paper we give necessary and suffici ent conditions that guarantee the existence, for any real, of an expan sion in base a with coefficients in D. Then we turn to balanced expans ions, for which the sums of the digits of any initial segment are unif ormly bounded. These issues yield necessary and sufficient conditions for stabilizing stationary linear discrete systems with a particular f amily of control jaws. (C) 1998 Academic Press.