Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties

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 H1 performance. The simulation results illustrate the effectiveness of the proposed methodology.