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Robust dissipative control for a class of uncertain linear discrete-time systems with time-delay. (Chinese. English summary) Zbl 1187.93027

Summary: Quadratic-dissipative control for linear discrete-time systems with time-delay is considered in this paper. Firstly, for the system without uncertainties, conditions are characterized for the systems to be asymptotically stable and stricty quadratic-dissipative. The output feedback dissipative control problem is then addressed, and methods for designing these controllers are also given. Secondly, as for uncertain systems, the considered structured uncertainty is characterized by a dissipative system. Robust quadratic-dissipative analysis is addressed. Dynamic output feedback controllers are developed so that the closed-loop system will achieve robust stability and strictly quadratic dissipativeness. Finally, the robust dissipative analysis and synthesis are respectively reduced to the dissipative analysis and synthesis problems without uncertainties. Results of the output feedback dissipative control can provide not only a unified framework for \(H^\infty\) control and passive control but also a more flexible and less conservative design for linear discrete-time systems with time-delay.

MSC:

93B35 Sensitivity (robustness)
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
93B36 \(H^\infty\)-control
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