BIBO STABILITY OF THE DISCRETE BILINEAR SYSTEM

The discrete-time bilinear system is investigated for bounded input bo unded output (BIBO) stability. The general state-space model is consid ered and two different sufficient conditions are established for BIBO stability. The bound on the state vector is also found for each case. The direct-form realization of the bilinear system is considered as a special case and a sufficient condition is derived for its stability. The necessary and sufficient condition is established for the stabilit y of the second order system. The derived conditions are useful for fi nding the range of the input sequence in order to guarantee a bounded output sequence. The results are illustrated with several examples. (C ) 1995 Academic Press,Inc.