Intrinsic difficulties in using the doubly-infinite time axis for input-output control theory

Points out that the natural definitions of stability and causality in input-output control theory lead to certain inconsistencies when inputs and outputs are allowed to have support on the doubly-infinite time-axis. In particular, linear time-invariant systems with right-half plane poles cannot be considered to be both causal and stabilizable. In contrast, there is no such conflict when the semi-infinite time axis is used.<
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