H _∞ control of networked control systems via discontinuous Lyapunov functionals

This chapter presents a new stability and L ₂-gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced in [13] and [12] in the framework of impulsive system representation. Most of the existing works on the stability of NCS (in the framework of time delay approach) are reduced to some Lyapunov-based analysis of systems with uncertain and bounded time-varying delays. This analysis via time-independent Lyapunov functionals does not take advantage of the sawtooth evolution of the delays induced by sample-and-hold. The latter drawback was removed in [4], where time-dependent Lyapunov functionals for sampled-data systems were introduced. This led to essentially less conservative results. The objective of the present chapter is to extend the time-dependent Lyapunov functional approach to NCS, where variable sampling intervals, data packet dropouts and variable network-induced delays are taken into account. The new analysis is applied to a novel network-based static output-feedback H _∞ control problem. Numerical examples show that the novel discontinuous terms in Lyapunov functionals essentially improve the results.