Abstract
Time-dependent Lyapunov functionals appeared to be very efficient for sampled-data systems. In [14], new Lyapunov functionals were constructed for sampled-data control in the presence of a constant input delay. The construction of these functionals was based on Wirtinger's inequality leading to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). In the present paper we extend the latter results to the discrete-time sampled-data systems. We show that the proposed approach is less conservative on some examples with a lower number of decision variables.
Highlights
Sampled-data systems have been studied extensively over the past decades
The continuous-time versions of this inequality have already shown their potential for the stability analysis of partial differential equation ([5]), sampled-data systems ([14]) or time-delay systems ([21])
The idea of this paper is to propose a dedicated construction of the functional to cope with the stability analysis of sampled and delayed closed-loop system driven by (2.1)
Summary
Sampled-data systems have been studied extensively over the past decades (see e.g. [1, 6, 17, 18, 8] and the references therein). Till [3] the conventional time-independent Lyapunov functionals V (xt , xt ) for systems with fastvarying delays were applied to sampled-data systems ([6]). These functionals did not take advantage of the sawtooth evolution of the delays induced by sampled-and-hold. The latter drawback was removed in [3] and [20], where time-dependent Lyapunov functionals (inspired by [18]) were constructed for sampled-data systems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
