Keywords: Networked control systems (NCS), control systems with delays, Lyapunov stability theory, asynchronous dynamical systems (ADS), linear and bilinear matrix inequalities (LMI and BMI). Abstract In this paper we study the stability of a networked control system using the stability theory of Lyapunov. The framework considered in this work is to allow in the discrete dynamics of the networked system unknown delays and some dropping in the samples between sensor and actuators. Solving a

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... r matrix inequality can demonstrate the stability of a system with time delays, and a bilinear matrix inequatily the stability with data dropping. As a case study, a simple integrator is used as a example.