## Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties.(English)Zbl 1198.93180

Summary: The problems of stability analysis and control synthesis for a class of neural systems with time-varying delays and nonlinear uncertainties are addressed. The dynamical system under consideration consists of different time-varying neutral and discrete delays without any restriction on upper bounds of derivatives of both delays. Based on the Lyapunov-Krasovskii functional theory, delay-dependent sufficient linear matrix inequalities (LMIs) conditions are established for the stability and stabilization of the considered system using some free matrices and the Leibniz-Newton formula. Control synthesis is to design a delayed state-feedback scheme based on a convex optimization method such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed level of $$H_{\infty }$$ performance. The simulation results illustrate the effectiveness of the proposed methodology.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

### MSC:

 93D15 Stabilization of systems by feedback 93B36 $$H^\infty$$-control 34K20 Stability theory of functional-differential equations

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