A Novel Discontinuous Lyapunov Functional Approach to Networked-Based Stabilization

This paper presents a new stability analysis of Networked Control Systems (NCSs), where the sampling and the constant network-induced delays are taken into account. The new method is inspired by discontinuous Lyapunov functionals that were recently introduced for sampled-data systems in [1] (in the framework of impulsive system representation) and in [2] (in the framework of input delay approach). However, extensions of the above Lyapunov constructions to NCSs lead to complicated conditions, which become conservative if the network-induced delays is not small. In the present paper a novel discontinuous Lyapunov functional is introduced, which is based on the application of the Wirtinger type inequality. This functional leads to efficient stability conditions in terms of Linear Matrix Inequality (LMIs). The new stability analysis is applied to sampled-data stabilization by using artificial delay.