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Dynamical compensation for time-delay systems: An LMI approach. (English) Zbl 0963.93073

The authors present robust stabilization of uncertain linear time-delay systems by observer-based controllers. The state observer contains a time delay which is not equal to the process’s one that makes the design problem realistic. Based on the Lyapunov-Krasowskij functional approach, the authors state a closed-loop stability sufficient condition in the form of a delay-independent linear matrix inequality. The conservatism of the condition may be relaxed by some refinements based on the IQC approach. Following the same line of reasoning the authors prove a sufficient condition for simultaneous closed-loop stabilization and global disturbance attenuation using a control-theoretic approach to \(H_\infty\) controllers design.
Less conservative, delay-dependent conditions could be obtained using the Razumikhin approach. In this case the linear matrix inequalities contain upper bounds of both time-delays (the one for the system and the, one for the controller). The proof is based on the transformation of the retarded functional differential equation into an integro-differential form and the use of the appropriate Lyapunov functional. If the delay bounds are not fixed then the sufficient condition for closed loop stability is not linear in the set of all variables but allowing for suboptimality of these bounds and using the Schur complement property, the problem may be once more solved by a linear matrix inequality.
The results are illustrated by numerical examples. The problem with the paper is that it contains a number of editorial errors and that some references have incomplete bibliographic data.

MSC:

93D21 Adaptive or robust stabilization
93C23 Control/observation systems governed by functional-differential equations
15A39 Linear inequalities of matrices
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