On the Stability Analysis of Sampled-Data Systems with Delays

Chapter
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 6)

Abstract

Controlling a system through a network amounts to solve certain difficulties such as, among others, the consideration of aperiodic sampling schemes and (time-varying) delays. In most of the existing works, delays have been involved in the input channel through which the system is controlled, thereby delaying in a continuous way the control input computed by the controller. We consider here a different setup where the delay acts in a way that the current control input depends on past state samples, possibly including the current one, which is equivalent to considering a discrete-time delay, at the sample level, in the feedback loop. An approach based on the combination of a discrete-time Lyapunov–Krasovskii functional and a looped-functional is proposed and used to obtain tailored stability conditions that explicitly consider the presence of delays and the aperiodic nature of the sampling events. The stability conditions are expressed in terms of linear matrix inequalities and the efficiency of the approach is illustrated on an academic example.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.LAAS-CNRSUniversité de Toulouse, CNRSToulouseFrance
  2. 2.Department of Biosystems Science and Engineering (D-BSSE)Swiss Federal Institute of Technology Zurich (ETH-Z)BaselSwitzerland

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