The problem of strict bounded realness for linear systems with finite discrete jumps is investigated in this paper. Several versions of the strict bounded real lemma for such systems in both the finite and infinite horizon cases are obtained in terms of either a Riccati differential equation or Riccati differential inequality with finite discrete jumps. These results encompass both existing continuous-time and discretetime strict bounded real lemmas.
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Shi et al. (1997) studied this question.
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