Stability analysis of a Networked Control Systems with time-varying delays using Parameter Dependant Lyapunov Function

The stability analysis of a Networked Control Systems (NCSs) with network induced time-varying delays presented in this article. The time-varying delays considered less than as well larger than sampling period. The uncertainties in the system arising with variations of the time-delays. The closed loop system is represented in discrete time domain. The uncertain closed loop system is modeled using polytopic approach. For stability, the static state feed back controller is used. The proposed Parameter Dependant Lyapunov Function (PDLF) stability criterion is compared with Quadratic Lyapunov Function (QLF) approach. The Lyapunov based stability criterion is represented in terms of Linear Matrix inequalities (LMIs). The stability region represented in terms of controller gain and maximum tolerable delay. The maximum tolerable delay found by solving LMIs for given different controller gains. The effectiveness of the proposed method is validated using two numerical examples.