Abstract
The discrete-time bilinear system is investigated for bounded input bounded output (BIBO) stability. The general state-space model is considered 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 stability of the second order system. The derived conditions are useful for finding the range of the input sequence in order to guarantee a bounded output sequence. The results are illustrated with several examples.
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