New bounded real lemma representations for time-delay systems and their applications

Emilia Fridman*, U. Shaked

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


New delay-dependent/delay-independent bounded real criteria are derived for linear continuous-time systems with delay in the dynamics and in the objective function. A sufficient condition for the system to possess a H-norm that is less than a prescribed level, is given in terms of a linear matrix inequality (LMI). The proposed criteria are less conservative than other existing criteria since they are based on an augmented model that is equivalent to the original system and since they require bounds for fewer terms. We apply the new bounded real criteria to state-feedback H control. The advantage of the new criteria is demonstrated by four examples. The first two compare our results with those obtained in the literature for the bounded real lemma and the other two examples treat the state-feedback control problem and compare our result with recently published designs.

Original languageEnglish
Pages (from-to)1973-1979
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 2001


FundersFunder number
Ministry of Absorption of Israel
Tel Aviv University


    • Bounded real lemma
    • Delay-dependent criteria
    • H-state-feedback control
    • Linear matrix inequalities (LMIs)
    • Time-delay systems


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