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Stability of DCESs Under the Hyper-Sampling Mode

  • Arben Çela
  • Mongi Ben Gaid
  • Xu-Guang Li
  • Silviu-Iulian Niculescu
Part of the Communications and Control Engineering book series (CCE)

Abstract

The main objective of this chapter is to understand the way in which periodic scheduling or hyper-sampling period and DCES-induced delays affect the stability of the controlled plant. Several scenarios are considered, leading to three stability problems. First, a delay-sweeping method is given in the case of constant parameters (hyper-sampling periods and DCES-induced delays). Next, two problems concerning the case when time-varying uncertain parameters are considered. For a system with time-varying uncertain parameters, a sufficient stability condition is given in terms of the existence of an appropriate Lyapunov matrix. The second problem concerns the stability of a real-time system including a constant hyper-sampling period and time-varying uncertain DCES-induced delays. In this case, sufficient conditions expressed in terms of feasibility of some appropriate linear matrix inequalities (LMIs) are proposed. Finally, the third problem concerns the case without DCES-induced delays but subject to time-varying uncertain hyper-sampling periods. The problem is handled by establishing an appropriate connection between the single-sampling and hyper-sampling cases. In this way, the hyper-sampling case appears as a direct application of the results derived in the single-sampling case. Next, a parameter-sweeping method is employed to detect the whole stability region in the corresponding parameter-space. Different examples (including also the case of two inverted pendulums) are given to illustrate the proposed results. It is worth mentioning that each system can be viewed as a switched system composed of “n” sub-systems if the hyper-sampling period has “n” sub-sampling periods. The derived stability regions include, in some cases, sub-regions where some sub-systems are not necessarily stable. This fact helps us to enlarge the stability ranges of the parameters by taking more advantage of the effect induced by the hyper-sampling period on the stability of the overall system. To the best of the authors’ knowledge, such an angle was not sufficiently addressed and exploited for real-time applications.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Arben Çela
    • 1
  • Mongi Ben Gaid
    • 2
  • Xu-Guang Li
    • 3
  • Silviu-Iulian Niculescu
    • 4
  1. 1.Department of Computer Science and TelecommunicationUniversité Paris-Est, ESIEE ParisNoisy-le-GrandFrance
  2. 2.Electronic and Real-Time Systems DepartmentIFP New EnergyRueil-MalmaisonFrance
  3. 3.School of Information Science and EngineeringNortheastern UniversityShenyangPeople’s Republic of China
  4. 4.L2S—Laboratoire des signaux et systèmesSupélecGif-sur-YvetteFrance

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