Abstract
Abstract Some basic connections between bounded-input, bounded-output stability and exponential asymptotic stability are presented for a class of linear time-varying hereditary systems. For that class of systems, controllability and observability are closely related to that of an equivalent linear system. This eases the analytical treatment of such properties which are then used to derive the stability results. The requirement of boundedness of inputs and outputs in the BIBO definition is modified by requesting that their ‘energy content’ over a fixed-length interval should be bounded independently of the position of the interval. For the class of hereditary linear systems studied, it is found that EAS and BIBO stability are equivalent under uniform complete controllability and observability.
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