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

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/sub /spl infin//-norm that is less than a prescribed level, is given in terms of a...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2001-12, Vol.46 (12), p.1973-1979
Main Authors: Fridman, E., Shaked, U.
Format: Article
Language:English
Subjects:
Absorption
Automatic control
Control systems
Criteria
Delay
Delay systems
Design engineering
Dynamical systems
Dynamics
Equivalence
Linear matrix inequalities
Partial differential equations
Representations
Riccati equations
Stability analysis
Stability criteria
Sufficient conditions
Symmetric matrices
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Summary: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/sub /spl infin//-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/sub /spl infin// 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.975503