Abstract
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.
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Liu, K., Fridman, E. (2012). H ∞ Control of Networked Control Systems via Discontinuous Lyapunov Functionals. In: Sipahi, R., Vyhlídal, T., Niculescu, SI., Pepe, P. (eds) Time Delay Systems: Methods, Applications and New Trends. Lecture Notes in Control and Information Sciences, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25221-1_33
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DOI: https://doi.org/10.1007/978-3-642-25221-1_33
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