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Delay-dependent robust \(H_\infty\) control for a class of uncertain nonlinear systems with time-varying delay. (English) Zbl 1212.93083

Summary: The problem of robust \(H_\infty\) control for a class of nonlinear systems with time-varying delays and time-varying norm-bounded parameter uncertainties is considered. The systems under consideration are also subject to exogenous bounded energy \(L_2\) disturbances. The attention is focused on the design of a full-order linear memoryless state feedback controller for the systems just mentioned above. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is given, which depends on the size of the delay.

MSC:

93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93B52 Feedback control
93C41 Control/observation systems with incomplete information