Stability analysis of networked control systems: A discontiuous lyapunov functional approach

This paper presents a new stability analysis of linear networked control systems. The new method is inspired by discontinuous Lyapunov functions that were introduced in [1] and [2] by using impulsive system representation of the sampled-data and of the networked control systems respectively. In the recent paper [3] piecewise-continuous (in time) Lyapunov-Krasovskii functionals have been suggested for the stability analysis of sampled-data systems in the framework of input delay approach. Differently from the existing Lyapunov functionals for systems with time-varying delays, the discontinuous ones can guarantee the stability under the sampling which may be greater than the analytical upper bound on the constant delay that preserves the stability. The objective of the present paper is to extend the discontinuous Lyapunov functional approach to networked control systems, where the sampling and the network-induced delays are taken into account. Our results depend on the upper bound of the network-induced delay and the improvement is achieved if the latter bound becomes smaller.